Model and Emergent Gravity

Muxin Han (韩慕⾟) (in collaboration with Zichang Huang (⻩⼦⾿) and Antonia Zipfel) General Relativity: Gravity = Curved Geometry

Quantum Gravity = Geometry

What is a Quantum Spacetime?

( In this talk, the spacetime dimension is 4 = 3+1 )

!2 Wheeler & Hawking’s Quantum Foam

J.A. Wheeler, and the issue of the final state, in Relativity, groups and topology, C. DeWitt and B.S. DeWitt eds., Gordon and Breach, New York U.S.A. (1964). S.W. Hawking, Space-time foam, Nucl. Phys. B 144 (1978) 349.

3 : If we localize too much a particle in spacetime, its energy and momentum grow. Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow.

General Relativity: If energy and momentum grow too much, it collapses and forms a .

Singularities, infinities, difficulies Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow.

General Relativity: If energy and momentum grow too much, it collapses and forms a black hole.

Singularities, infinities, difficulies

Resolution: There is a minimal scale (Planck scale p) in spacetime against localization. Quantum Spacetime is Foam-like

A minimal cell of quantum spacetime A Complementary Point of View: Emergent Gravity

Quantum Gravity as an Ocean of Entangled Qubits

Xiao-Gang Wen, Zhenghan Wang 2018 Zheng-Cheng Gu, Xiao-Gang Wen 2009

!8 A Complementary Point of View: Emergent Gravity

Quantum Spacetime is a Tensor Network

Swingle 2009, Evenbly, Vidal, 2014 Pastawski, Yoshida, Harlow, Preskill, 2015 Hayden, Nezami, Qi, Thomas, Water, Yang 2016 Qi, Yang 2018 !9 Question Quantum of Emergent Spacetime is Foam-like Gravity (Semiclassical Consistency of QG Model)

A minimal cell of quantum spacetime Foam-like spacetime Ocean of entangled qubits

Quantum, Discrete, and Algebraic (fundamental)

Classical Gravity: Smooth Spacetime Geometry (emergent low energy excitations)

!10 Spin Foam Model (SFM) and Emergent Gravity

The definition of SFM as a State-Sum Model and a Tensor Network

Large Spin Asymptotics and Emergent Geometry

Continuum limit and Emergent () Einstein Equation

Gµ⌫ = 0

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

!11 Spin Foam Model and Covariant Quantum Spacetime is Foam-like Foam-like discrete spacetime: a triangulation of 4-manifold (simplicial complex)

A MinimalA spacetime minimal Cell cell in Loop of Quantumquantum Gravity spacetime

4-simplex4-simplex:: the simplest cell in 4dminimal cell in 4d triangulation (10 triangles and 5 tetrahedra) 4-dimensional analog of tetrahedron in 3d and triangle in 2d.

Quantum spacetime is formed by gluing many ~ ~ 4-simplicesSpin Foam 4-simplex amplitude 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 A(J, I)

10 triangles 10 SU(2) spins J Z+/2

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 f

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 f Loop Quantum Gravity: 2 Each 4-simplex is associated with a "4-simplex amplitude"

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 5 tetrahedra ⌧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 5 SU(2) invariant tensors A function of area and volume quanta I⌧ Inv [V V ] 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 2 SU(2) j1 ⌦ ···⌦ j4

12 A triangulation of 4-manifold Spin Foam Model as a state-sum Gluing many 4-simplices: spacetime foam 4-simplex amplitude

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face amplitude: A = 2J + 1

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Spin Foam Amplitude in LQG: spins 4-simplex amplitude: Engle, Pereira, Rovelli, Livine, 2007

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 A = tr(i i ) 1 ⌦ ···⌦ 5 sum over all weight product over all 4-simplices intermediate states = , C 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 SL(2 ) 15j symbol (fusion coe cients) ⇥

SL(2,C) invariant tensor: SL(2,C) Wigner D-matrix

4 ( jk, jk) m1 m4 i = dg k=1 D(l ,m ),( j ,m )(g) I ··· C ⌦ k0 k0 k k 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 ZSL(2, ) 4-simplex amplitude is a linear map of 5 invariant tensors: 5 ⌦ A : InvSU(2)[V j1 V j4 ] C 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 ⌦ ···⌦ ! ⇣ ⌘ !13 Spin Foam Model as a Tensor Network

4-simplex amplitude is a linear map of 5 invariant tensors:

5 ⌦ A : InvSU(2)[V j1 V j4 ] C 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 ⌦ ···⌦ ! 4-simplex amplitude is ⇣a tensor state (of 5 invariant tensors)⌘

5 ⌦ A InvSU(2)[V j1 V j4 ] |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 i2 ⌦ ···⌦ ⇣ ⌘ Gluing two 4-simplices = inner product with an EPR state of a pair of invariant tensors : the simplest cell in 4d

: the simplest cell in 4d 4-simplex 4-dimensional analog of tetrahedron in 3d and 4-simplex triangle in 2d. 4-dimensional analog of tetrahedron in 3d and Quantum spacetime is formed by gluing many A Minimal spacetime Cell in Looptriangle Quantum in 2d. Gravity 4-simplices

Quantum spacetime is formed by gluing many 4-simplices

A Minimal spacetime Cell in Loop Quantum Gravity

"4-simplex amplitude"

"4-simplex amplitude"

Loop Quantum Gravity: Each 4-simplex is associated with a Loop Quantum Gravity: Each 4-simplex is associated with a

A function of area and volume quanta A function of area and volume quanta

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A | i⌦h | 0

h | 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 | i XI

!14 Spin Foam Model as a Tensor Network Gluing many 4-simplices: spacetime foam Gluing many 4-simplices: spacetime foam

spin sum (spin dependent) tensor network Spin Foam Amplitude in LQG: spins Z( )Spin= Foam AAmplitude(J ) ine LQG:A spins K f f ⌦e h | ⌦ | i ~ f AAAlT3icnZpJc9y4FYB7JtuMsnmSYy5IZJXbGVlWy3ZmaiqTmpZkWbIlS7YWL6LUBZJgk25wEQi2Foq/Lb8hx1xyyzU55pbKA0h2Y2nJrrTK3SC+9x4WPjw8gnYzGuV8efnvn33+ox//5Kc/++LLuZ//4pe/+vWdr35zlKcF88ihl9KUvXVxTmiUkEMecUreZozg2KXkjTtaE/zNmLA8SpMDfpmRkxgPkyiIPMyhanDn3fuu443uf+/kRTwonTHxyudV5WQs9QcB6g+C7vNBcN9BTsqjmOSDklQOxcmQEkTQdVvr5NEQXYO4KDhM8sGd+eWlZflBdqHXFOY7zWdv8NX8Pxw/9YqYJNyjOM+Pe8sZPykx45FHSTXnFDnJsDfCQ3IMxQRD0yelnIMKLUCNj4KUwb+EI1mrapQ4zvPL2AXJGPMwN5monMWOCx58e1JGSVZwknh1Q0FBEU+RmFDkR4x4nF5CAXssgr4iL8QMexymfW5uZjtQvaDW52F6TrFLaF7ZYEQu82oBhZxn3z186HGcLKVs+DAbDR+2eM5uR45VqxwynIWRd7FYz9jMni3CLw9jXZFfiCnNDQ0hzvJAVKtdPs69E8kyfJXqozk+6J2UwpSYR6HFSELOvTSOceL/0eHcJwEuKC+9eMx5ZQkEOI7oZSs0lYd7soB2E7gFUYB4SJBYELUbpHVF61YoysV9c4m8dedwtwhDOb+k5LaOqqN2Y9Fz+4MyoLUpNAPDZ85JfT+PfBJjNowSWAFPvHjO4WnWVCzLigVHLOVcLGK/7C09glvByQU/j3weot63XozQAur9qa4NSTQMOVp5UlevPJ7VtY9/5pzpNJcO86tjGL8jbqKHaTnfqypd4jUJpEgXblAg+H1DgGI6nBoJGB5JK9DF7YgggMRlWFdJ0kp8JUXsEuY4YBDurpMk08qmKigdMOg1V5gx6LGYBSil50Y/YoKTuh91zBK9aMKTcC9VFDqkSiIhem0KjQiXQtdovocmhvShZzAOQikEUxajPXPq/Cio6llhcelblLBoXB2vnNRjlOLQVNUUVkB+QTh0ykgMIa4AD4UglxPelMuceDBZPskgyJRPauuNfHlQ/1aTwjFIi13gRBNbJ0GURKK+UsuzhbcJ9Lw6biyeNNcLs4XXUpZSitllpRRni+6xNEvzpuWJdbXWaGMyhTk4AoftKxXzLNaIGwi9NPgONjFkTrgYXh624mEQUYruOqvpxV0kfVCVfd/cONct31srYspem2xtytYq06MO2NQdoGyo5mmlLCG4Mjjc5NKBNYo2LcNbLdqqRAjTtDAVo5UeBr5Ve9UG7JzgZAGBmMsj0ANdr6BFjiA0FUmRF1CXQxgkueGzaQHJRu20oRQol5d64F5yjTQ14LrqZS1gOr9L69VRW2zWyoPlpcdPZgp7KUsIU+Qpa6uE0kydc+IPiaLSXIP8N9/O7hGhiniCXYprcVsaQnvCp8I9Kfeo7vvMPcPcQjD10xs2jxkxW1hE/dXV10+PtvoHW7sv92WNkntovVu/Jew8nTJiMulHEMkiE6yvC9JsEmjdxNgFDF9GtQvTV8KXUd1vbeUeK/uViTeUpsoNC3OpziO4WzOU+caU2rqu1HXxrGbdjZbZemv7wPYHMsSUcCEWEUx/UCQyKuXGcsyHSROPSlE0V6sXthRKZhCYsNxifDiBfAacsKHJZNyRzI46sK+NWirL9dBERplSw60K6QVFAjuXyFscyw/etbcOnOtdNXCGWOwQhtALeYdEey9uEtnfXl9TTO1vV92VxWlcvW/NGvU9IV9HTloNVpQgbNo+FPfysLtiWWmzgj+L6HVtQC0b+IuZeogF4FAS8K7jEsjv4DmGYdj64BHC8dLcga2O4wGsE9hp4LEpUSsIWKjF69zGzK+e32b9gW4NrBvNfcx6LBbpJ3TdxXrPXfwpPb/F+APdmt7zG6x/PLLKh0IeQuovnyQhWH1igDVcQSxgSMNJiHmzoQclxDdI9DgKLMeBbeN6tWGm47jjqn7UXr1BO0rG0/QZvH0LrgeNhx7P904McShPI7i4MHPSdIq3TUiKKXxqwlGUTOmLKLFyiX3qVbcsSl14T5Pe+5h4LqWD3Amotnp1qcOznE6NHlaDs66tY5s+07oNSrf1hDeN1JvItK0bGzNnSZljCDbiNhr9KZqRFoMVC51pyqKrpjp0r5g1B2DtE5YIwr5PfOReop3iArK9T1oecoksIMSJFyZyVWHXZWQc4Xr7qx/PXJitepWTs6Reuc2DGwEilrNSL3eZNUxp1BxVoD7NQuwSbkynh6tp5tE3XdJzFbpqzJTnKXDNhH6lZjQGJAp8asJAgRsmHCrwmQlDBW6aMFLglgk/KPC5CUcKfGFCqsBtE8YK3DFhosCXJkwVuGvCTIF7JjxT4CsTYsoU/NrEuQL3TcgVeGDCQoGHJhwr8MiE5wp8Y8ILBb414aUC35nwSoHvmwUBGXGU8ZuWQt4uhSZxNmis0J12iW1ASsQLdpPJoDUpUydIxBDSk3GNW20GropdW13jq5a6p2LPVte4tRsEvop9W13jVrYaEBUTW13j1nYZBCoObHWNb1jqQxUPbXWNP7PUQxWHtrrGNy11qI1UiUhYkB/djCm3ZVn6oOIPdkc0/txSH6l4ZKtr/IWlTlVMbXWNW/lQEKs4ttU1vmOpJypObHWNv7TUtROf1FbX+K6lnqk4s9U1bp1OBmcqPrPVNf7K9iAVM1td49ZBWZCrOLfVNb5vqXMVc1td4weWeqHiwlbX+KGlPlbx2FbX+JGlfq7ic1td428s9QsVX9jqGn9rqV+q+NJW1/g7S/1KxVe2usbfWw8Rngx8fsqRCIEG25iwDYt5E+ZZLGIyQRK0fVxDVqgRUsKrxC8lvpk+fIjT1mmE9mn5oNduos8YISNECa9f82mvqkpHbJFYbK+VScTuB3suNloSA6nPPfT6Z1D/rKnXDYmNzCfUskQyMaAxZlCIaJrYWMS/CdTPoaSaoa5LcHngFMoRGEfZghyE9tjAmNSSvzY+avDRbJxHYm7g25qbfUn2G6LPjhgjxbHr22gbAdtumD4EEZ9YmFoqIuimMRnaxnaB7M4kwnE4Low+i5VwZQ9yJBxmhLMMm2uDxW3GwmLkmyc18kkInT5wfg9/nmk1a/DXN2AC4fzU2csjyeXf9+bRgRiGOK0xzwhFvTyDMcDmy0q8YeCQX3Rfms+pmztTuGPB8QQOxlbaTCfrsFyDC7ObeNj0s3l/Zx1pDtv+zn5t15/Octm3Dsi58paGW+elrtvmpLPOJ/ri/U86rs9Hp6fYkDefqkqmFpuOt2+1WCjHKIfd3v3q9JEh0U50a2PHaiHPosmR9D6Uu4+t089ImZTImpS9VDl3ERcG3yiUsyNxYU5bNh2ilYlg+eTGQtPjfczl+SHvfhiI1wuL/cXm8H7RuYjqqiv5Ay5qephQThvt07K7fL9qbNQXraX2qrHXXF4pF7Nsi1Cs9O5ebRr177Vm700s3muM3Zthx8XeaMjSIvHVYTZ9GA7w/9W5+u1Dcyvq9w96hL4tPrM4Utxg1sss1Dxims+m7bYvnj5h1x/cme+Z///HLhytLPWWl3qvHs//sNr836AvOr/r/KHT7fQ633R+6Gx29jqHHa/z184/O//q/Pvu3+7+5+5/FxrRzz9rCr/taJ+FL/8HQqQPWg== XJ Y

e = Ie Ie sum over all weight product over all 4-simplices | i | i⌦| i

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 I intermediate states sume over all weight product over all 4-simplices Xintermediate states

Spin Foam Model is an Ocean of Entangled Qubits (Qudits)

!15 Spin Foam Model (SFM) and Emergent Gravity

The definition of SFM as a State-Sum Model and a Tensor Network

Large Spin Asymptotics and Emergent Geometry

Continuum limit and Emergent (vacuum) Einstein Equation

Gµ⌫ = 0

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

!16 Integral Representation of the Tensor Network, Spin Foam Asymptotics

Gluing many 4-simplices: spacetime foam Z( ) = A (J ) e A K f f ⌦e h | ⌦ | i ~ f 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 XJ Y

Integration variables 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 X C 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g SL(2, ) “half edge” holonomy ve 2 z CP1 spinors at vertices 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vf 2

The regimeSpin where Foam classical Amplitude spacetime in LQG: geometry emergesspins from the model: Large-J regime

2 LQG area spectrum: a f = 8⇡`P J f (J f + 1)

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Classical (discrete) spacetime geometries = solutions of EOM

EOM: Geometrical interpretation of variables, geometrical reconstruction Freidel, Conrady 2008 Barrett et al, 2009 MH, Zhang, 2011 !17 The Discrete Geometry from Spin Foam Model: Regge Geometry

A Minimal spacetime Cell in Loop Quantum Gravity

4-simplex: the simplest cell in 4d 4-dimensional analog of tetrahedron in 3d and triangle in 2d.

Quantum spacetime is formed by gluing many 4-simplicesflat interior geometry

Loop Quantum Gravity: Each 4-simplex is associated with a "4-simplex amplitude"

curvedA function of area and volumegeometry quanta are made by gluing geometrical 4-simplices of different shapes

Geometries are charactered by discrete metric: edge lengths `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 `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

discrete curvature: Deficit angle at co-dimension-2 hinges

deficit angle "AAAk+HicnZpJc9y4Fcd7JttE2TzJMRckkspyRpbVsp1xTSWp0WJZsiVLthYvotQFkmCTbnARCLYWml8h1+SYWyrXfJtc8lnyAJJNLC3ZlVa5m8Tv/R8B8OEBBO1mNMr58vJ/vvjyBz/80Y9/8tVPZ37281/88ld3vv71cZ4WzCNHXkpT9tbFOaFRQo54xCl5mzGCY5eSN+5oXfA3Y8LyKE0O+VVGTmM8TKIg8jAXRQ7J8sGd2eWlZflB9kG/OZjtNZ/9wdez/3X81CtiknCP4jw/6S9n/LTEjEceJdWMU+Qkw94ID8kJHCY4JvlpKStboXko8VGQMviXcCRLVUWJ4zy/il2wjDEPc5OJwmnspODBk9MySrKCk8SrLxQUFPEUiZYjP2LE4/QKDrDHIqgr8kLMsMehf2Zmpl4HiufV8jxMLyh2Cc0rG4zIVV7No5Dz7LsHDzyOk6WUDR9ko+GDFs/Y15Ft1QqHDGdh5F0u1j02tWaL8MvDWBfyS9GluaEQ5iwPRLFa5ZPcO5Usw9ep3pqTw/5pKVyJfhQqRhJy4aVxjBP/Dw7nPglwQXnpxWPOK8sgwHFEr1qjzh7uyTzaS+AWRAHiIUEicuswSOuCNqxQlIv75hJ56y7gbhGGcn5FyW0VVVvtxqLm9gdlQGtXaAqGz4yT+n4e+STGbBglMAIee/GMw9OsKViWBfOOGHO5GG1+2V96CLeCk0t+Efk8RP0nXozQPOr/sS4NSTQMOVp5XBevPJpWtU9/Zpyum0uH+dUJtN8RN9HDtJztV5Vu8ZoE0mQBblAg+D3DgGI67JwEDI+kF6jiTkQQQOIyrEuStBJfSRG7hDkOOIS76yRJV9gUBaUDDr3mDDMGNRa9AEfphVGPmOCkrgfFyZASUQuHyUMRXqopVEi1RML0o2k0IlwafUSzfTRxpDc9g3YQSgdQrRjtm13nR0FV9wqLS9+ihEXj6mTltG6jNIdLVc3BCtjPi4BOGYkhxRUQoZDkcsKb4zInHnSWTzJIMuXj2ntjXx7Wv9Xk4ASsRbo+1cw2SBAlkSiv1OPpxjsEal6dNB5Pm/P56cbrKUspxeyqUg6nm+6zNEvz5soT72qpcY1JF+YQCDxjaSr6WYwRNxC6NPjOQQ4yO1w0Lw9b8zCIKEVzzlp6OYdkDKq275sb57rle2tEdOy1ydY7tl6ZEXXIunCAY0Oap5UyhODM4HCTSwfGKNqyHG+3aLsSKUxTYSpaKyMMYquOqk2YOSHIAgI5l0egA61X0CJHkJqKpMgLKMshDZLciNm0gFVBHbShNCiXl/oQXnKMNCUQuuppbWAGv0vr0VF7bMbK/eWlR4+nGnspSwhT7Clri4RoquaC+EOiSJpzsP/2yfQaEaqYJ9iluDa3rSG1J7wz7ku7h3Xdp84Z5hSCqZ/eMHlMydnCI1pdW3v99Hh79XB77+WBLFHWHlrtNm5JO087Rkwm4wgyWWSCjQ1BmkkCbZgYu4Dhyyh2oftK+DKKV1tfucfK1crEm8qlyk0LcynnEdytKWK+2VFb60qti6dd1t1sma1bPwB2MJAppoQTMYig+4MikVkpN4ZjPkyafFSKQ3O0emFL4chMAhOWW4wPJ5BPgRM2NJnMO5LZWQfmtVFL5XHdNLGiTKkRVoWMgiKBmUusWxwrDt61tw6C6101cIZYzBCG0Qt5h8T1XtxkcrCzsa64OtipFlYWu7x6z+o16nvCvs6ctBqsKEnY9H0k7uXRworlpV0V/Elkr48G1FYDfzGXHmIAOJQEfMFxCazv4DmGYZj64BHC8dLcgamO4wGME5hpnDxK1AICHmrzem1jrq+e3+b9vu4NvBuX+5T3WAzSz6i6i/Wau/hzan6L8/u6N73mN3j/dGaVD4U8hKW/fJKEZPWZCdYIBTGAYRlOQsybCT0oIb/BQo+jwAocmDY+rjXMDBx3DK7GxCvXblBHybhbPkO0b8P5oInQk9n+qWEOx10GFyfmmjTt8I4JSdHBpyYcRUlHX0SJtZY4oF51y6DUjfc16/1PmefSOsidgGqjV7c6Os9p5/SoGpwv2Brb9blWbRDdVhPeXKSeRLpr3Xgxs5eUPoZkI26jUZ+iaWkxWLHQuSYWVTXlUL1iWh+At88YIgj7PvGRe4V2i0tY7X3W8JBDZB4hTrwwkaMKuy4j4wjX01/9eOZCb9WjnJwn9chtHtwIEDGclXI5y6xjSqNmqwKt0izELuFGd3q46lYeq2ZIeq5C14ye8jwFrpvQr9QVjQGJAp+aMFDgpgmHCnxmwlCBWyaMFLhtwg8KfG7CkQJfmJAqcMeEsQJ3TZgo8KUJUwXumTBT4L4JzxX4yoSYMgW/NnGuwAMTcgUemrBQ4JEJxwo8NuGFAt+Y8FKBb014pcB3JrxW4PtmQMCKOMr4TUMhb4dCs3A2aKzQ3XaIbcKSiBfsJpdB61IunWAhhpC+GNe4dc3AVbFryzW+Zsk9FXu2XOPWbBD4KvZtucat1WpAVExsucat6TIIVBzYco1vWvKhioe2XOPPLHmo4tCWa3zLkkNppFpEwoP86G5Mu23L0wcVf7ArovHnlnyk4pEt1/gLS05VTG25xq31UBCrOLblGt+15ImKE1uu8ZeWXNvxSW25xvcseabizJZr3NqdDM5VfG7LNf7KjiAVM1uucWujLMhVnNtyjR9Ycq5ibss1fmjJCxUXtlzjR5Z8rOKxLdf4sSW/UPGFLdf4G0t+qeJLW67xt5b8SsVXtlzj7yz5tYqvbbnG31sPEZ5MfH7KkUiBBtucsE2LeRPmWSxicoEkaPu4hqxUI6xEVIlfSnxz+fAhTtugEeqz8n6/nUSfMUJGiBJev+bTXlWVjpgisZheK5OI2Q/mXGxcSTSk3vfQy59B+bOmXHckJjKfUMsTyUSDxpjBQUTTxMYi/02gvg8lZYZct+BywymULTC2sgU5DO22gTOpkr82Pm7w8XScR6Jv4NvqmwNJDhqi945oI8Wx69toBwHbaZjeBJGfWJhaEpF005gMbWd7QPamEhE4HBdGncVIuLYbORIBM8JZhs2xweJ2xcJi5Js7NfJJCJ3dd34Hf57pNWvwNzdgAun8zNnPI8nl35/NrQPRDLFbY+4RinK5B2OArZeVeMPAYX2x8NJ8Tt3a7eCuBccTOBhby2Y6GYflOpyY1cTDpp7N+ztrS3PY1nf6a7vVrpfLVWuDnCtvabi1X+q67Zp02v7Eqnj/k47r/dFuFxvWzWeqyFSxrr2r1hULZRvlaKF/rzp7aFi0Hd362LWukGfRZEv6AI4XHlm7n5HSKZHVKfupsu8iTgy+WSh7R+LE7Lasa6K1EsHyyY2FZsT7mMv9Q77wYSBeLyyuLjab94vOZVQXXcsfCFEzwoQ4bdRn5cLyvarxUZ+0ntqzxl9zeq2cTPMtUrFSu7u1a7R6t3V7d+LxbuPs7hQ/LvZGQ5YWia82s6nDcID/r8rVbx+aW1G/f9Az9G35mcWREgbTXmah5hHTfDZtp33x9Amz/uDObN/8/z/2wfHKUn95qf/q0ez3a83/Dfqq99ve73sLvX7v2973va3efu+o5/XC3l97f+v9fe567h9z/5z7V2365ReN5jc97TP37/8BMDHuSA==

By refining the triangulation, the discrete geometries converge to smooth geometries

!18 Spin Foam Asymptotics Gluing many 4-simplices: spacetime foam

Z( ) = A (J ) e A K f f ⌦e h | ⌦ | i ~ f AAAlT3icnZpJc9y4FYB7JtuMsnmSYy5IZJXbGVlWy3ZmaiqTmpZkWbIlS7YWL6LUBZJgk25wEQi2Foq/Lb8hx1xyyzU55pbKA0h2Y2nJrrTK3SC+9x4WPjw8gnYzGuV8efnvn33+ox//5Kc/++LLuZ//4pe/+vWdr35zlKcF88ihl9KUvXVxTmiUkEMecUreZozg2KXkjTtaE/zNmLA8SpMDfpmRkxgPkyiIPMyhanDn3fuu443uf+/kRTwonTHxyudV5WQs9QcB6g+C7vNBcN9BTsqjmOSDklQOxcmQEkTQdVvr5NEQXYO4KDhM8sGd+eWlZflBdqHXFOY7zWdv8NX8Pxw/9YqYJNyjOM+Pe8sZPykx45FHSTXnFDnJsDfCQ3IMxQRD0yelnIMKLUCNj4KUwb+EI1mrapQ4zvPL2AXJGPMwN5monMWOCx58e1JGSVZwknh1Q0FBEU+RmFDkR4x4nF5CAXssgr4iL8QMexymfW5uZjtQvaDW52F6TrFLaF7ZYEQu82oBhZxn3z186HGcLKVs+DAbDR+2eM5uR45VqxwynIWRd7FYz9jMni3CLw9jXZFfiCnNDQ0hzvJAVKtdPs69E8kyfJXqozk+6J2UwpSYR6HFSELOvTSOceL/0eHcJwEuKC+9eMx5ZQkEOI7oZSs0lYd7soB2E7gFUYB4SJBYELUbpHVF61YoysV9c4m8dedwtwhDOb+k5LaOqqN2Y9Fz+4MyoLUpNAPDZ85JfT+PfBJjNowSWAFPvHjO4WnWVCzLigVHLOVcLGK/7C09glvByQU/j3weot63XozQAur9qa4NSTQMOVp5UlevPJ7VtY9/5pzpNJcO86tjGL8jbqKHaTnfqypd4jUJpEgXblAg+H1DgGI6nBoJGB5JK9DF7YgggMRlWFdJ0kp8JUXsEuY4YBDurpMk08qmKigdMOg1V5gx6LGYBSil50Y/YoKTuh91zBK9aMKTcC9VFDqkSiIhem0KjQiXQtdovocmhvShZzAOQikEUxajPXPq/Cio6llhcelblLBoXB2vnNRjlOLQVNUUVkB+QTh0ykgMIa4AD4UglxPelMuceDBZPskgyJRPauuNfHlQ/1aTwjFIi13gRBNbJ0GURKK+UsuzhbcJ9Lw6biyeNNcLs4XXUpZSitllpRRni+6xNEvzpuWJdbXWaGMyhTk4AoftKxXzLNaIGwi9NPgONjFkTrgYXh624mEQUYruOqvpxV0kfVCVfd/cONct31srYspem2xtytYq06MO2NQdoGyo5mmlLCG4Mjjc5NKBNYo2LcNbLdqqRAjTtDAVo5UeBr5Ve9UG7JzgZAGBmMsj0ANdr6BFjiA0FUmRF1CXQxgkueGzaQHJRu20oRQol5d64F5yjTQ14LrqZS1gOr9L69VRW2zWyoPlpcdPZgp7KUsIU+Qpa6uE0kydc+IPiaLSXIP8N9/O7hGhiniCXYprcVsaQnvCp8I9Kfeo7vvMPcPcQjD10xs2jxkxW1hE/dXV10+PtvoHW7sv92WNkntovVu/Jew8nTJiMulHEMkiE6yvC9JsEmjdxNgFDF9GtQvTV8KXUd1vbeUeK/uViTeUpsoNC3OpziO4WzOU+caU2rqu1HXxrGbdjZbZemv7wPYHMsSUcCEWEUx/UCQyKuXGcsyHSROPSlE0V6sXthRKZhCYsNxifDiBfAacsKHJZNyRzI46sK+NWirL9dBERplSw60K6QVFAjuXyFscyw/etbcOnOtdNXCGWOwQhtALeYdEey9uEtnfXl9TTO1vV92VxWlcvW/NGvU9IV9HTloNVpQgbNo+FPfysLtiWWmzgj+L6HVtQC0b+IuZeogF4FAS8K7jEsjv4DmGYdj64BHC8dLcga2O4wGsE9hp4LEpUSsIWKjF69zGzK+e32b9gW4NrBvNfcx6LBbpJ3TdxXrPXfwpPb/F+APdmt7zG6x/PLLKh0IeQuovnyQhWH1igDVcQSxgSMNJiHmzoQclxDdI9DgKLMeBbeN6tWGm47jjqn7UXr1BO0rG0/QZvH0LrgeNhx7P904McShPI7i4MHPSdIq3TUiKKXxqwlGUTOmLKLFyiX3qVbcsSl14T5Pe+5h4LqWD3Amotnp1qcOznE6NHlaDs66tY5s+07oNSrf1hDeN1JvItK0bGzNnSZljCDbiNhr9KZqRFoMVC51pyqKrpjp0r5g1B2DtE5YIwr5PfOReop3iArK9T1oecoksIMSJFyZyVWHXZWQc4Xr7qx/PXJitepWTs6Reuc2DGwEilrNSL3eZNUxp1BxVoD7NQuwSbkynh6tp5tE3XdJzFbpqzJTnKXDNhH6lZjQGJAp8asJAgRsmHCrwmQlDBW6aMFLglgk/KPC5CUcKfGFCqsBtE8YK3DFhosCXJkwVuGvCTIF7JjxT4CsTYsoU/NrEuQL3TcgVeGDCQoGHJhwr8MiE5wp8Y8ILBb414aUC35nwSoHvmwUBGXGU8ZuWQt4uhSZxNmis0J12iW1ASsQLdpPJoDUpUydIxBDSk3GNW20GropdW13jq5a6p2LPVte4tRsEvop9W13jVrYaEBUTW13j1nYZBCoObHWNb1jqQxUPbXWNP7PUQxWHtrrGNy11qI1UiUhYkB/djCm3ZVn6oOIPdkc0/txSH6l4ZKtr/IWlTlVMbXWNW/lQEKs4ttU1vmOpJypObHWNv7TUtROf1FbX+K6lnqk4s9U1bp1OBmcqPrPVNf7K9iAVM1td49ZBWZCrOLfVNb5vqXMVc1td4weWeqHiwlbX+KGlPlbx2FbX+JGlfq7ic1td428s9QsVX9jqGn9rqV+q+NJW1/g7S/1KxVe2usbfWw8Rngx8fsqRCIEG25iwDYt5E+ZZLGIyQRK0fVxDVqgRUsKrxC8lvpk+fIjT1mmE9mn5oNduos8YISNECa9f82mvqkpHbJFYbK+VScTuB3suNloSA6nPPfT6Z1D/rKnXDYmNzCfUskQyMaAxZlCIaJrYWMS/CdTPoaSaoa5LcHngFMoRGEfZghyE9tjAmNSSvzY+avDRbJxHYm7g25qbfUn2G6LPjhgjxbHr22gbAdtumD4EEZ9YmFoqIuimMRnaxnaB7M4kwnE4Low+i5VwZQ9yJBxmhLMMm2uDxW3GwmLkmyc18kkInT5wfg9/nmk1a/DXN2AC4fzU2csjyeXf9+bRgRiGOK0xzwhFvTyDMcDmy0q8YeCQX3Rfms+pmztTuGPB8QQOxlbaTCfrsFyDC7ObeNj0s3l/Zx1pDtv+zn5t15/Octm3Dsi58paGW+elrtvmpLPOJ/ri/U86rs9Hp6fYkDefqkqmFpuOt2+1WCjHKIfd3v3q9JEh0U50a2PHaiHPosmR9D6Uu4+t089ImZTImpS9VDl3ERcG3yiUsyNxYU5bNh2ilYlg+eTGQtPjfczl+SHvfhiI1wuL/cXm8H7RuYjqqiv5Ay5qephQThvt07K7fL9qbNQXraX2qrHXXF4pF7Nsi1Cs9O5ebRr177Vm700s3muM3Zthx8XeaMjSIvHVYTZ9GA7w/9W5+u1Dcyvq9w96hL4tPrM4Utxg1sss1Dxims+m7bYvnj5h1x/cme+Z///HLhytLPWWl3qvHs//sNr836AvOr/r/KHT7fQ633R+6Gx29jqHHa/z184/O//q/Pvu3+7+5+5/FxrRzz9rCr/taJ+FL/8HQqQPWg== XJ Y

Spin Foam Amplitude in LQG: spins Large-J asymptotics of the integral: Evaluating the action at the critical point i = " J f F f [Xc] 2 a f f MH, Zhang, 2011 `P 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 f Xf sum over all weight product over all 4-simplices intermediate states Regge action: Discrete version of Einstein-Hilbert action d4 x p gR

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i a f " f Large-J asymptotics of the integral: J F [X] `2 f [dX] e f f f e P P AAAlW3icnZpbc9u4Fce1u71s3W2bbadPfUHr1cRpHcfyJt2dnbazthMnTuzEG19yMW0NSIIiI/BiAJQvDD9hP0Ef2u/Q1/alByAp4SI7mcoTicTv/A8B8OAABOMXNOFidfUfn3z62Y9+/JOffv6zhZ9/8Ytf/urWl78+4nnJAnIY5DRnr33MCU0ycigSQcnrghGc+pS88sebkr+aEMaTPDsQlwU5SfEoS6IkwAKKhreIl2TCo+LYY2mIXntMnHjL5LTyeJkOq6h+OozQ1jCSFgrWHk9SJA0ihoMqqSuPUDrcO12rO4mXYhH7UYVr0JGCD6N6eGtxdWVVfZB7MGgPFnvtZ2/45eK/vDAPypRkIqCY8+PBaiFOKsxEElBSL3glJwUOxnhEjuEwwynhJ5Xqjxr1oSREUc7gXyaQKtUVFU45v0x9sJR15TaThfPYcSmib0+qJCtKQbKguVBUUiRyJDsXhQkjgaCXcIADlkBdURBj6CgBt2BhYe51oLivl/M4P6fYJ5TXLhiTS173USxE8d29e4HA2UrORveK8ehehxfc66i2GoUjhos4CS6Wmx6bW7Nl+BVxagrFhexSbimkOeORLNarfMyDE8UKfJWbrTk+GJxU0pXsR6liJCPnQZ6mOAv/6AkRkgiXVFRBOhGidgwinCb0sjOa2cM96aMXGdyCJEIiJkgOjiYM8qagCyuUcHnffKJu3TncLcIQF5eU3FRRvdV+KmvuflABtHGF5mD4LHh5GPIkJClmoySDEfAgSBc8kRdtwaoq6HtyWHM5oMNqsPI13ApBLsR5EooYDb4NUoT6aPDnpjQmySgWaO1BU7x2f17VPvxZ8GbdXHksrI+h/WpIB5hWi4O6Ni1ekkiZLMENiiS/YxlQTEczJ5A1xsoLVHEnIQgg8Rk2JVley6+sTH3CPA8cwt31smxW2BZFTRpqzzBjUGPZC3CUn1v1SAnOmnpQnI0okbXwmDqU4aWbQoV0SyRN39tGYyKU0Xu0OEBTR2bTizY9QrVStGd3XZhEddMrLK1ChxKWTOrjtZM21UpzuFTdHqyBfV8GdM5ICimuhAiFJMeJaI8rTgLorJAUkGSqB4331r46aH7r6cExWMsZ4cQwe0iiJEtkea0fzzfeIVDz+rj1eNKe9+cbb+YspxSzy1o7nG+6x/Ii5+2Vp971Uusa0y7kEAiiYHku+1mOEZiV9uTpdx7ykN3hsnk87szjKKEUfeVt5BdfIRWDuu3b9sb5fvXWGREz9tJmmzO2WdsRdcBm4QDHlpTntTaE4MzicJMrD8YoeuI43u7Qdi1TmKHCVLZWRRjEVhNVWzBzQpBFBHKuSEAH2qCkJUeQmsqs5CWUcUiDhFsxm5ew8GiCNlYG1erKAMJLjZG2BEJXP20M7OD3aTM6Go/tWLm7unL/wVzjIGcZYZo9ZV2RFM3VnJNwRDRJew7233w7v0aEauYZ9iluzF1rSO2ZmBkPlN3XTd3nzhn2FIJpmF8zeczJ2dIjWt/YePnoaHv9YPvF831Voq09jNo9vCHtPJoxYjMVR5DJEhs8fChJO0mghzbGPmD4sop96L4Kvqzi9c4XD1i1Xtt4S7tUteVgoeQigbs1Ryy2ZtTV+krr43mX9bc65uo294HtD1WKqeBEDiLo/qjMVFbi1nDko6zNR5U8tEdrEHcUjuwkMGXcYWI0hWIOnLKRzVTeUczNOjCvjTuqjpumyRVlTq2wKlUUlBnMXHLd4jlx8Ka7dRBcb+qhN8JyhrCMnqk7JK/37DqT/Z2Hm5qr/Z16aW15llfvOL1Gw0DaN5mT1sM1LQnbvg/lvTxcWnO8dKuCv8js9d6Cxmrgb/bSQw4Aj5JILHk+gfUdPMcwDFMfPEJ4Qc49mOoEHsI4gZkGHrAyvYCAh8a8WdvY66unN3m/a3oD79blPuQ9lYP0I6ruY7PmPv6Ymt/g/K7pzaz5Nd4/nFnVQ6GIYemvniQhWX1kgrVCQQ5gWIaTGIuqe96F/AYLPYEiJ3Bg2ni/0TI7cPwJuJqQoNq4Rp1kk9nyGaJ9G86HbYQeLw5OLHM4nmVweWKvSfMZ3rEhKWfwkQ3HSTajz5LMWUvs06C+YVCaxnuG9d6HzLmyjrgXUWP0mlaHZ5zOnB7Ww7MlV+O6PjOqDaKbaiLaizSTyOxa117M7iWtjyHZyNto1adsW1oO1xx0ZohlVW05VK+c1wfg7SOGCMJhSELkX6Ld8gJWex81PNQQ6SMkSBBnalRh32dkkuBm+msez3zorWaUk7OsGbntgxsBIoezVq5mmU1MadJuVaB1WsTYJ8LqzgDXs5XHuh2Sga/RDaungkCDmzYMa31FY0GiwUc2jDS4ZcORBh/bMNbgExsmGty24TsNPrXhWIPPbEg1uGPDVIO7Nsw0+NyGuQZf2LDQ4J4NzzT4gw0xZRp+aWOuwX0bCg0e2LDU4KENJxo8suG5Bl/Z8EKDr214qcE3NrzS4Nt2QMCKOCnEdUOBd0OhXThbNNXobjfEtmBJJEp2ncuoc6mWTrAQQ8hcjBvcuWbk69h35QbfcOSBjgNXbnBnNohCHYeu3ODOajUiOiau3ODOdBlFOo5cucG3HPlIxyNXbvDHjjzWcezKDf7EkUNpolsk0oP6mG5su23H0zsdv3MrYvCnjnys47ErN/gzR051TF25wZ31UJTqOHXlBt915JmOM1du8OeO3NjxyV25wV848kLHhSs3uLM7GZ3p+MyVG/wHN4J0zFy5wZ2NsojrmLtyg+87cqFj4coNfuDISx2Xrtzgh458ouOJKzf4kSM/1/G5Kzf4K0d+oeMLV27w1478UseXrtzgbxz5lY6vXLnB3zoPEYFKfGEukEyBFtuasi2HBVMWOCxhaoEkafe4hpxUI61kVMlfSkJ7+fAuzbugkerT6u6gm0QfM0LGiBLRvOYzXlVVnpwisZxea5vI2Q/mXGxdSTak2fcwyx9D+eO23HQkJ7KQUMcTKWSDJpjBQULzzMUy/02huQ+lZJbctBBqwylWLbC2siU5iN22gTOlUr8uPmrx0XzME9k38O30zb4i+y0xe0e2keLUD120g4DttMxsgsxPLM4diUy6eUpGrrMXQF7MJTJwBC6tOsuRcOU2ciwDZoyLAttjg6XdioWlKLR3atSTEDq96/0e/gLba9HiP12DCaTzU2+PJ4qrv7/aWweyGXK3xt4jlOVqD8YCT57X8g2DgPXF0nP7OfXJ7gzuOnAyhcOJs2ym03FYbcKJXU08auvZvr9ztjRHXX3nv7Zbn/Vyte5skAvtLY1w9kt9v1uTztufWJfvf/JJsz8628WGdfOpLrJVbNbedeeKpbaNcrg0uFOffm1ZdB3d+dh1rsCLZLolvQ/HS/ed3c9E65TE6ZS9XNt3kScW3yq1vSN5YndbMWuisxLB6smNxXbEh1io/UOx9G4oXy8sry+3m/fL3kXSFF2pHwhRO8KkOG/Vp9XS6p269dGcdJ66s9Zfe3qlnczzLVOxVrvbjWu0frtze3vq8Xbr7PYcPz4OxiOWl1moN7Otw2iI/6/KNW8f2lvRvH8wM/RN+ZmliRYG815mofYR03427aZ9+fQJs/7w1uLA/v8/7sHR2spgdWXww/3F7zfa/xv0ee93vT/0lnqD3je973tPenu9w17Q+3vv373/9P771T/7n/UX+l80pp9+0mp+0zM+/d/+D//QFIs= ⇠ Z P

!19 Spin Foam Model (SFM) and Emergent Gravity

The definition of SFM as a State-Sum Model and a Tensor Network

Large Spin Asymptotics and Emergent Geometry

Continuum limit and Emergent (vacuum) Einstein Equation

Gµ⌫ = 0

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!20 Continuum limit

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 µ continuum limit:

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 1 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 1/2 K K ··· K ···

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K K ··· K ···

discrete geometries discrete geometries discrete geometries 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 on on on

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1 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 1/2 µ K K 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 ···

Semiclassical continuum limit: The flow of parameters: J(µ), ↵ (µ), (µ)

AAAlFnicnZpJc9y4FYB7JttE2TzJMRckksrtjCyrZTszNZWkpiVZlmzJkq3Fiyh1gSTYpBtcBIKtheY1vyE/ItfkmFsq11xzyW/JA0h2Y2nJrrTK3SC+9x6xPDw8gnYzGuV8ZeU/n33+ve//4Ic/+uLHcz/56c9+/os7X/7yOE8L5pEjL6Upe+PinNAoIUc84pS8yRjBsUvJa3e0LvjrMWF5lCaH/CojpzEeJlEQeZhD1eAOetZ14uLekoMcPAgmZZ9QjuXV4M78yvKK/CC70GsK853msz/4cv6/jp96RUwS7lGc5ye9lYyflpjxyKOkmnOKnGTYG+EhOYFigmOSn5ayKxVahBofBSmDfwlHslbVKHGc51exC5Ix5mFuMlE5i50UPPjmtIySrOAk8eobBQVFPEViXJAfMeJxegUF7LEI2oq8EDPscRi9ubmZ94HqRbU+D9MLil1C88oGI3KVV4so5Dz79sEDj+NkOWXDB9lo+KDFc/Z9ZF+1yiHDWRh5l0v1iM1s2RL88jDWFfmlGNLc0BDiLA9Etdrkk9w7lSzD16nem5PD3mkpTIlxFFqMJOTCS+MYJ/7vHM59EuCC8tKLx5xXlkCA44hetUJTeZiTRbSXwBREAeIhQcKvazdI64rWrVCUi3lziZy6C5gtwlDOryi5raFqr91YtNz+oAxobQrNwPCZc1LfzyOfxJgNowRWwGMvnnN4mjUVK7Ji0RErMhdr0S97yw9hKji55BeRz0PU+8aLEVpEvd/XtSGJhiFHq4/r6tVHs5r28c+cMx3m0mF+dQL9d8QkepiW872q0iVekUCKdGGCAsHvGQIU0+HUSMDwSFqBJu5EBAEkLsO6SpJW4ispYpcwxwGDMLtOkkwrm6qgdMCg11xhxqDFYhSglF4Y7YgJTup2UJwMKRGtcJgsCvdSRaFBqiQSoh9MoRHhUugDmu+hiSG96xn0g1A6gGbFaN8cOj8KqnpUWFz6FiUsGlcnq6d1H6U43KpqCqsgvygcOmUkhhBXgIdCkMsJb8plTjwYLJ9kEGTKx7X1Rr48rH+rSeEEpEUwP9XENkgQJZGor9TybOEdAi2vThqLp8314mzh9ZSllGJ2VSnF2aL7LM3SvLnzxLpaa9xjMoQ5OALPWJqKcRZrxA2EXhp8C7sTMgdcdC8PW/EwiChFC85aermApA+qsu+aiXPd8p21IqbslcnWp2y9Mj3qkE3dAcqGap5WyhKCK4PDJJcOrFG0ZRnebtF2JUKYpoWp6K30MPCt2qs2YecEJwsIxFwegR7oegUtcgShqUiKvIC6HMIgyQ2fTQvIGWqnDaVAubLcA/eSa6SpAddVL2sB0/ldWq+O2mKzVu6vLD96PFPYS1lCmCJPWVsllGbqXBB/SBSV5hrkv/5mdosIVcQT7FJci9vSENoTPhXuSbmHddtn7hnmFoKpn96wecyI2cIi6q+tvXpyvN0/3N57cSBrlNxDa93GLWHnyZQRk0k/gkgWmWBjQ5Bmk0AbJsYuYPgyql0YvhK+jOp+ayv3WNmvTLyp3KrctDCX6jyC2ZqhzDen1NZ1pa6LZ93W3WyZrbd+AOxgIENMCRdiEcHwB0Uio1JuLMd8mDTxqBRFc7V6YUuhZAaBCcstxocTyGfACRuaTMYdyeyoA/vaqKWyXHdNZJQpNdyqkF5QJLBzibzFsfzgbTt14Fxvq4EzxGKHMISeyxkS93t+k8jBzsa6Yupgp+quLk3j6j1r1KjvCfk6ctJqsKoEYdP2kZjLo+6qZaXNCv4gotcHA2rZwJ/M1EMsAIeSgHcdl0B+B88xDMPWB48QjpfmDmx1HA9gncBO4+RRolYQsFCL17mNmV89u836fd0aWDdu9zHrsVikn9B0F+std/GntPwW4/d1a3rLb7D+8cgqHwp5CKm/fJKEYPWJAdZwBbGAIQ0nIebNhh6UEN8g0eMosBwHto0Paw0zHccdg6kx8cq1G7SjZDxNn8Hbt+F60HjoyXzv1BCH8jSCiwszJ02neMeEpJjCJyYcRcmUPo8SK5c4oF51y6LUhfc16f2PiedSOsidgGqrV5c6Os/p1OhRNTjv2jq26XOt2aB0W0t4c5N6E5ne68abmaOkjDEEGzGNRnuKpqfFYNVC55qyaKqpDs0rZo0BWPuEJYKw7xMfuVdot7iEbO+TlodcIosIceKFiVxV2HUZGUe43v7qxzMXRqte5eQ8qVdu8+BGgIjlrNTLXWYdUxo1RxWoT7MQu4Qbw+nhapp59E2X9FyFrhkj5XkKXDehX6kZjQGJAp+YMFDgpgmHCnxqwlCBWyaMFLhtwvcKfGbCkQKfm5AqcMeEsQJ3TZgo8IUJUwXumTBT4L4JzxX40oSYMgW/MnGuwAMTcgUemrBQ4JEJxwo8NuGFAl+b8FKBb0x4pcC3JrxW4LtmQUBGHGX8pqWQt0uhSZwNGit0t11im5AS8YLdZDJoTcrUCRIxhPRkXOPWPQNXxa6trvE1S91TsWera9zaDQJfxb6trnErWw2IiomtrnFruwwCFQe2usY3LfWhioe2usafWuqhikNbXeNbljrURqpEJCzIj27GlNu2LL1X8Xu7IRp/ZqmPVDyy1TX+3FKnKqa2usatfCiIVRzb6hrftdQTFSe2usZfWOraiU9qq2t8z1LPVJzZ6hq3TieDcxWf2+oaf2l7kIqZra5x66AsyFWc2+oaP7DUuYq5ra7xQ0u9UHFhq2v8yFIfq3hsq2v82FK/UPGFra7x15b6pYovbXWNv7HUr1R8Zatr/K2lfq3ia1td4++shwhPBj4/5UiEQINtTtimxbwJ8ywWMZkgCdo+riEr1Agp4VXilxLfTB/ex2nrNEL7rLzfazfRp4yQEaKE16/5tFdVpSO2SCy218okYveDPRcbdxIdqc899PqnUP+0qdcNiY1Mvm01n+cy0aExZlCIaJrYWMS/CdTPoaSaoa5LcHngFMoeGEfZghyGdt/AmNSSvzY+bvDxbJxHYmzg2xqbA0kOGqKPjugjxbHr22gHAdtpmN4FEZ9YmFoqIuimMRnaxvaA7M0kwnE4Low2i5VwbXdyJBxmhLMMm2uDxW3GwmLkmyc18kkInd13fgN/nmk1a/BXN2AC4fzM2c8jyeXfH82jA9ENcVpjnhGKenkGY4CtF5V4w8Ahv+i+MJ9Tt3ancNeC4wkcjK20mU7WYbkOF2Yz8bBpZ/P+zjrSHLbtnf3arj8d5bJvHZBz5S0Nt85LXbfNSWedT/TF+590XJ+PTk+xIW8+U5VMLTbtb9+6Y6Ecoxx1e/eqs4eGRDvQrY1d6w55Fk2OpA+g3H1knX5GyqBE1qDsp8q5i7gw+GahnB2JC3PYsmkXrUwEyyc3Fpoe72Muzw959/1AvF5Y6i81h/dLzmVUV13LH3BR08OEctpon5XdlXtVY6O+aC21V4295vJauZhlW4RipXV3a9Oof7c1e3di8W5j7O4MOy72RkOWFomvdrNpw3CA/6/G1W8fmqmo3z/oEfq2+MziSHGDWS+zUPOIaT6bttu+ePqEXX9wZ75n/v8fu3C8utxbWe69fDT/3Vrzf4O+6Py689tOt9PrfN35rrPV2e8cdbzOnzt/7fyt8/eFvyz8Y+GfC/+qRT//rNH5VUf7LPz7f9a3+Bw= f

2 1 dJ 1 d fs quantum corrections satisfying: lim J(µ) < min | | in SFM µ 1 s m+1 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 0 µ µ µ !1 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 J d  s f d !   | s|

lim ↵ f (µ) = 0 shrink the lattice spacing µ 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 0 ! MH, 2013 lim (µ) = 0 µ µ 1 MH, 2017 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 J( ) ( ) 1 µ 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 0 !

/ bound of deficit angle: " (µ) (µ)1 2 |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 f | 

!21 Continuum limit

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 AAAk+nicnZpJc9y4Fcd7JttE2TzJMRckkspyRpbVsp1xTSWp0WLZsiVLthYvotQFkmCTanARCLYWmt8h1+SYWyrXfJlc8lnyAJJNLC3ZlVa5m8Tv/R8B8OEBBO1mNMr58vJ/vvjyBz/80Y9/8tVPZ37281/88ld3vv71UZ4WzCOHXkpT9s7FOaFRQg55xCl5lzGCY5eSt+5oXfC3Y8LyKE0O+FVGTmI8TKIg8jCHoiPH81OeD+7MLi8tyw+yD/rNwWyv+ewNvp79r+OnXhGThHsU5/lxfznjJyVmPPIoqWacIicZ9kZ4SI7hMMExyU9KWd0KzUOJj4KUwb+EI1mqKkoc5/lV7IJljHmYm0wUTmPHBQ+enJRRkhWcJF59oaCgiKdItB35ESMep1dwgD0WQV2RF2KGPQ49NDMz9TpQPK+W52F6QbFLaF7ZYESu8moehZxn3z144HGcLKVs+CAbDR+0eMa+jmyrVjhkOAsj73Kx7rGpNVuEXx7GupBfii7NDYUwZ3kgitUqH+feiWQZvk711hwf9E9K4Ur0o1AxkpALL41jnPh/cDj3SYALyksvHnNeWQYBjiN61Rp19nBP5tFuArcgChAPCRKxW4dBWhe0YYWiXNw3l8hbdwF3izCU8ytKbquo2mo3FjW3PygDWrtCUzB8ZpzU9/PIJzFmwyiBEfDYi2ccnmZNwbIsmHfEqMvFePPL/tJDuBWcXPKLyOch6j/xYoTmUf+PdWlIomHI0crjunjl0bSqffoz43TdXDrMr46h/Y64iR6m5Wy/qnSLNySQJgtwgwLB7xkGFNNh5yRgeCS9QBW3I4IAEpdhXZKklfhKitglzHHAIdxdJ0m6wqYoKB1w6DVnmDGosegFOEovjHrEBCd1PShOhpSIWjhMHorwUk2hQqolEqYfTaMR4dLoI5rto4kjvekZtINQOoBqxW

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 µ continuum limit:

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 1 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 1/2 K K ··· K ···

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K K ··· K ···

discrete geometries discrete geometries discrete geometries Smooth geometries on on on

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 1 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 1/2 µ K K 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

Semiclassical continuum limit: The flow of parameters: J(µ), ↵ (µ), (µ)

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2 1 dJ 1 d fs quantum corrections satisfying: lim J(µ) < min | | in SFM µ 1 s m+1 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0 µ µ µ !1 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 J d  s f d !   | s|

lim ↵ f (µ) = 0 shrink the lattice spacing µ 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 0 ! MH, 2013 lim (µ) = 0 µ µ 1 MH, 2017 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 J( ) ( ) 1 µ 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 0 !

/ bound of deficit angle: " (µ) (µ)1 2 |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 f | 

!22 Gluing many 4-simplices: spacetime foam

Z( ) = A (J ) e A Kµ f f ⌦e h | ⌦ | i ~ f 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 XJ Y

Under theSpin semiclassical Foam Amplitude continuum in LQG: limit: spins

i i 4 a f (µ)" f (µ) d x p gR[1+✏(µ)] J F [X] `2 f µ2`2 [dX] e f f f e P = e P P R 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 ⇠ Z P The lowsum overenergy all effectiveweight theoryproduct of spin over allfoam 4-simplices model is Einstein gravity 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 µ 0 ! intermediate states

Schematically:

i d4 x p gR[1+✏(µ)] µ2`2 A f Dgµ⌫ sum over geometries Z( µ) Dgµ⌫ e P R

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 K ⇠ ~ f 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 J Y Z Z

equation of motion: Einstein equation MH, 2013 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 µ 0 Gµ⌫ = 0 ! 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 MH, 2017

!23 Conclusion

The Spin Foam Model, as a model in Covariant Loop Quantum Gravity, can be understood as a Tensor Network model, or an ocean of entangled qubits. Gluing many 4-simplices: spacetime foam

Semiclassical consistency of SFMSpin Foam = emergentAmplitude in LQG: gravity fromspins SFM

sum over all weight product over all 4-simplices Indeed we show that under the SFM semiclassicalintermediate states continuum limit

i d4 x p gR[1+✏(µ)] µ2`2 P

Z( µ) Dgµ⌫ e 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 µ 0 R 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 K ⇠ ! Z

We find SFM is a good candidate of quantum gravity model (emergent gravity model)

!24 Conclusion

The Spin Foam Model, as a model in Covariant Loop Quantum Gravity, can be understood as a Tensor Network model, or an ocean of entangled qubits. Gluing many 4-simplices: spacetime foam

Semiclassical consistency of SFMSpin Foam = emergentAmplitude in LQG: gravity fromspins SFM

sum over all weight product over all 4-simplices Indeed we show that under the SFM semiclassicalintermediate states continuum limit

i d4 x p gR[1+✏(µ)] µ2`2 P

Z( µ) Dgµ⌫ e 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 µ 0 R AAAlYHicnZpZd9u4FceV6Za6yyTtW/uC1tGJMuM4lpN0cua0PeMljj2xEydespi2DkiCIi1wMQjKC8Pv2Ne+9KEfoq/tBUhKWGQnp/KJROJ3/5cAeHEBgnEzGuV8aemft776yU9/9vNf3P7l3K9+/Zvffn3n7u8O87RgHjnwUpqy9y7OCY0ScsAjTsn7jBEcu5S8c0drgr8bE5ZHabLPLzNyHONhEgWRhzkUDe6cfuw53mjgxMUDJ49i5EQJR+vDQQklTlJUDiInpRMw7JVRJQpPlh1C6WD3ZLkStg6L/ZMnF86Ck58xXj4cguKtg4763zokyyOaJj3h+xhVaHBnfmlxSX6QfdBvDuY7zWd3cHf+X46fekVMEu5RnOdH/aWMH5eY8cijpJpzipxk2BvhITmCwwTHJD8uZadUqAslPgpSBv+gTbJUVZQ4zvPL2AXLGPMwN5konMWOCh48Oy6jJCs4Sbz6QkFBEU+R6GHkR4x4nF7CAfZYBHVFXoihBznch7m5mdeB4q5anofpOcUuoXllgxG5zKsuCjnPvn/0yOM4WUzZ8FE2Gj5q8Zx9HdlWrXDIcBZG3sVC3WMza7YAvzyMdSG/EF2aGwphzvJAFKtVPsq9Y8kyfJXqrTna7x+XwpXoR6FiJCHnXhrHOPG/cTj3SYALyksvHnNeWQYBjiN62RpN7eGedNHrBG5BFCAeEiRGSB0GaV3QhhWKcnHfXCJv3TncLcJQzi8puamiaqvdWNTc/qAMaO0KzcDwmXNS388jn8SYDaMERsBTL55zeJo1BUuyoOuIsZ2LUe2X/cXHcCs4ueDnkc9D1H/mxQh1Uf8vdWlIomHI0fLTunj5yayqff4z50y7uXSYXx1B+x1xEz1My/l+VekWb0kgTXpwgwLBHxgGFNPh1Amkk5H0AlXcjggCSFyGdUmSVuIrKWKXMMcBh3B3nSSZFjZFQZ2fmjPMGNRY9AIcpedGPWKCk7oeFCdDSkQtHCYPRXipplAh1RIJ00+m0YhwafQJzffRxJHe9AzaIVImVCtGu2bX+VFQ1b3C4tK3KGHRuDpaPm5ysDCHS1XNwTLYd0VAp4zEkOIKiFBIcjnhzXGZEw86yycZJJnyae29sS/3699qcnAE1mJaONbM1kkQJZEor9Tj2cbbBGpeHTUej5vz7mzjtZSllGJ2WSmHs013WZqleXPliXe11LjGpAtzCASesTQV/SzGiBsIXRp87yAHmR0umpeHrXkYRJSie85qenEPyRhUbT82N851y4/WiJiytyZbm7K1yoyofTYNBzg2pHlaKUMIzgwON7l0YIyiTcvxVou2KpHCNBWmorUywiC26qjagJkTgiwgkHN5BDrQegUtcgSpqUiKvICyHNIgyY2YTQtYfdRBG0qDcmmxD+Elx0hTAqGrntYGZvC7tB4dtcdmrDxcWnzydKaxl7KEMMWesrZIiGZqzok/JIqkOQf7757NrhGhinmCXYprc9saUnvCp8Z9afe4rvvMOcOcQjD102smjxk5W3hEK6urb58fbq3sb71+tSdLlLWHVrv1G9LO8ykjJpNxBJksMsH6uiDNJIHWTYxdwPBlFLvQfSV8GcUrra/cY+VKZeIN5VLlhoW5lPMI7tYMMd+YUlvrSq2LZ13W3WiZrVvbA7Y3kCmmhBMxiKD7gyKRWSk3hmM+TJp8VIpDc7R6YUvhyEwCE5ZbjA8nkM+AEzY0mcw7ktlZB+a1UUvlcd00saJMqRFWhYyCIoGZS6xbHCsOPrS3DoLrQzVwhljMEIbRS3mHxPVeXmeyt72+prja2656ywvTvPrA6jXqe8K+zpy0GiwrSdj0fSDu5UFv2fLSrgr+KrLXJwNqq4G/m0sPMQAcSgLec1wC6zt4jmEYpj54hHC8NHdgquN4AOMEZhp4FkvUAgIeavN6bWOur368yftD3Rt4Ny73Oe+xGKRfUHUX6zV38ZfU/AbnD3Vves2v8f75zCofCnkIS3/5JAnJ6gsTrBEKYgDDMpyEmDcTelBCfoOFHkeBFTgwbXxabZgZOO4YXI2JV65eo46S8XT5DNG+BeeDJkKP5vvHhjkcTzO4ODHXpOkUb5uQFFP43ISjKJnSl1FirSX2qFfdMCh1413Nevdz5rm0DnInoNro1a0OznI6dXpQDc56tsZ2faZVG0Q31YQ3F6knkem1rr2Y2UtKH0OyEbfRqE/RtLQYLFvoTBOLqppyqF4xqw/A2xcMEYR9n/jIvUQ7xQWs9r5oeMgh0kWIEy9M5KjCrsvIOML19Fc/nrnQW/UoJ2dJPXKbBzcCRAxnpVzOMmuY0qjZqkArNAuxS7jRnR6upiuPFTMkPVehq0ZPeZ4C10zoV+qKxoBEgc9NGChww4RDBb4wYajATRNGCtwy4akCfzThSIEvTUgVuG3CWIE7JkwU+MqEqQJfmzBT4K4JzxT4xoSYMgW/NXGuwD0TcgXum7BQ4IEJxwo8NOG5At+Z8EKB7014qcAPJrxS4MdmQMCKOMr4dUMhb4dCs3A2aKzQnXaIbcCSiBfsOpdB61IunWAhhpC+GNe4dc3AVbFryzW+ask9FXu2XOPWbBD4KvZtucat1WpAVExsucat6TIIVBzYco1vWPKhioe2XOMvLHmo4tCWa3zTkkNppFpEwoP86G5Muy3L06mKT+2KaPxHSz5S8ciWa/ylJacqprZc49Z6KIhVHNtyje9Y8kTFiS3X+CtLru34pLZc468teabizJZr3NqdDM5UfGbLNf7GjiAVM1uucWujLMhVnNtyje9Zcq5ibss1vm/JCxUXtlzjB5Z8rOKxLdf4oSU/V/G5Ldf4O0t+oeILW67x95b8UsWXtlzjHyz5lYqvbLnGP1oPEZ5MfH7KkUiBBtuYsA2LeRPmWSxicoEkaPu4hqxUI6xEVIlfSnxz+XAap23QCPVJ+bDfTqIvGCEjRAmvX/Npr6pKR0yRWEyvlUnE7AdzLjauJBpS73vo5S+g/EVTrjsSE5lPqOWJZKJBY8yaF7I2FvlvAvV9KCkz5LoFlxtOoWyBsZUtyH5otw2cSZX8tfFhgw9n4zwSfQPfVt/sSbLXEL13RBspjl3fRtsI2HbD9CaI/MTC1JKIpJvGZGg7ew3k9UwiAofjwqizGAlXdiNHImBGOMuwOTZY3K5YWIx8c6dGPgmhk4fOn+DPM71mDf72GkwgnZ84u3kkufz7m7l1IJohdmvMPUJRLvdgDLD5qhJvGDisL3qvzOfUzZ0p3LHgeAIHY2vZTCfjsFyDE7OaeNjUs3l/Z21pDtv6zn5ttzLt5XLF2iDnylsabu2Xum67Jp21P7Ei3v+k43p/dLqLDevmE1Vkqti0vSvWFQtlG+Wg139QnTw2LNqObn3sWFfIs2iyJb0Hx70n1u5npHRKZHXKbqrsu4gTg28Uyt6RODG7LZs20VqJYPnkxkIz4n3M5f4h750OxOuFhZWFZvN+wbmI6qIr+QMhakaYEKeN+qTsLT2oGh/1SeupPWv8NadXysks3yIVK7W7X7tGK/dbt/cnHu83zu7P8ONibzRkaZH4ajObOgwH+P+qXP32obkV9fsHPUPflJ9ZHClhMOtlFmoeMc1n03baF0+fMOsP7sz3zf//Yx8cLi/2lxb7b57M/7Da/N+g250/dv7c6XX6ne86P3Q2O7udg47X+UfnP53/3urc+3f3dvfr7t3a9Ktbjeb3He3T/cP/AGohEp0= K ⇠ ! Z

We find SFM is a good candidate of quantum gravity model (emergent gravity model)

Thanks for your attention !

!25 !26 !27 backup slides

!28 Resolve the tension between large J and continuum limit (small area)

µ 1 is a length unit

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such that lim ↵ f (µ) = 0 for the continuum limit of the geometry µ 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 0 !

!29 Mathematically Rigorous Story

i d4 x p gR[1+✏(µ)] µ2` Z( µ) Dgµ⌫ e P is not rigorous because path integral is not well defined R 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 K ⇠ Z Rigorously, on each triangulation, we obtain a Regge equation from variating Regge action

discrete Einstein equation Regge, 1961

bound of deficit angle: " (µ) (µ)1/2 from SFM |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 f | 

continuum limit of Regge equation SFM semiclassical continuum limit 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 µ 0 !

There is no general proof converges to smooth Einstein equation due to non-linearity

But there is no counter-example. All known examples of solutions demonstrate the convergence.

The situation is similar to the Numerical Relativity, where one can obtain arbitrary with discrete data.

Some mathematically rigorous results by using the convergence of Regge solutions (case by case study):

On the flat background, the only low energy excitations SFM are gravitational waves (spin-2 )

The highly curved Einstein solutions: e.g. Kasner universe MH, Zichang Huang, Antonia Zipfel, to appear MH, Hongguang Liu, to appear

!30 Conclusion

The Spin Foam Model, as a model in Covariant Loop Quantum Gravity, can be understood as a Tensor Network model, or an ocean of entangled qubits. Gluing many 4-simplices: spacetime foam

Semiclassical consistency of SFMSpin Foam = emergentAmplitude in LQG: gravity fromspins SFM

sum over all weight product over all 4-simplices Indeed we show that under the SFM semiclassicalintermediate states continuum limit (IR limit)

i d4 x p gR[1+✏(µ)] µ2`2 P

Z( µ) Dgµ⌫ e 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 µ 0 R 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 K ⇠ ! Z

Convergence of solutions in the limit: spin-2 gravitons and Kasner universe (solutions of Einstein equation)

We find SFM is a good candidate of quantum gravity model (emergent gravity model)

To do: more Einstein solutions, quantum corrections, etc……

!31 An open issue

There might exists disjoint “superselection sectors” in SFM other than Einstein solutions.

parameter space of SFM non-Einstein solutions

Einstein solutions

non-Einstein non-Einstein solutions solutions

Different sectors are not connected by continuous deformation of SFM solutions.

!32 An open issue

There might exists disjoint “superselection sectors” in SFM other than Einstein solutions.

parameter space of SFM non-Einstein solutions

Einstein solutions

non-Einstein non-Einstein solutions solutions

Different sectors are not connected by continuous deformation of SFM solutions.

The end

Thanks for your attention !

!33 Integral Representation of the Tensor Network, Spin Foam Asymptotics

Gluing many 4-simplices: spacetime foam Z( ) = A (J ) e A K f f ⌦e h | ⌦ | i ~ f 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 XJ Y

Integration variables 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X C 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g SL(2, ) “half edge” holonomy ve 2 z CP1 spinors at vertices 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 vf 2 TheSpin equations Foam Amplitude of motion in(critical LQG: equations)spins from the action tell that the integration variables have the geometrical interpretation.

C 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 g SL(2, ) relates to the spin connection parallel transport ve 2 z CP1 sum over all weight product over all 4-simplices 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vf relates to the tetrahedron faces normals 2 intermediate states (tetrahedron geometry)

Critical equation: geometrical tetrahedra are parallel transported and glued.

The integration variables satisfying the critical equations can reconstruct a 4d discrete geometry on the triangulation. Freidel, Conrady 2008 Barrett et al, 2009 MH, Zhang, 2011 !34 Gluing many 4-simplices: spacetime foam

Spin Foam Amplitude in LQG: spins

!35 sum over all weight product over all 4-simplices intermediate states