Black Holes, Holography and Strings Harvard University Department Of

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Black Holes, Holography and Strings

A Celebration of the Science of Andrew Strominger

Harvard University Department of Physics

July 3031, 2015

Black Holes, Holography and Strings July 3031, 2015

Main Page About Andy Talks Directions Hotel Information Contacts

(Photo: H. Ooguri)

This conference aims to bring together a diverse group of physicists and educators whose career paths have intersected with Andy's and who share his passion for Physics.

In addition to talks scheduled for Thursday, July 30 and Friday, July 31, there will be a banquet on Thursday evening. Please see the conference schedule for more details. S. Pasterski July 30, 2015 1 / 9 O 1 i) Weinberg – photon ( ω ) O 1 ii) Weinberg – graviton ( ω ) iii) Cachazo & Strominger – graviton O(1)

Soft Factors

Memories Symmetries

(global) (asymptotic) i) Li´enard-Wiechert / Bieri & Garﬁnkle i) e-charge large U(1) ii) Zeldovich & Polnarev / Christodoulou ii) pµ supertranslations iii) Pasterski, Strominger, & Zhiboedov iii) J µν superrotations

July 30, 2015 2 / 9

1 Radiation Memory)4

Az Measurable observable: ∂zΦIII ∂zΦII Finite energy ﬂux i +

Massive charges Propagating to r >> rs ∂zΦI + I Radiation u 1 I Far-ﬁeld r n fall-offs i 0 I = 0@u !±1 = 0 generic u Large r observer 6 - du... = 0 I 6 R i -

S. Pasterski July 30, 2015 3 / 9 Consistency of fall-off conditions allowing radiation , local on S2 shift in baseline value of O

Radiation Memory – Symmetry)4

∂zΦIII

∂zΦII Memory 1 du frad (u) i +

⌘ Massive charges 1 ∂zΦI I measure ﬁnite net effect + R 2 I Radiation u I observer anywhere on S

i 0 u O(u) du0 f (u0) u0 rad Large r observer ⌘ I - I Mem = O(u ) O(u ) s.t. f (u )=0 Reff f i rad i,f u = How long should I wait? i - f 6 1 u = Did something happen before? i 6 1

S. Pasterski July 30, 2015 4 / 9 Radiation Memory – Symmetry)4

∂zΦIII

∂zΦII Memory 1 du frad (u) i +

⌘ Massive charges 1 ∂zΦI I measure ﬁnite net effect + R 2 I Radiation u I observer anywhere on S

i 0 u O(u) du0 f (u0) u0 rad Large r observer ⌘ I - I Mem = O(u ) O(u ) s.t. f (u )=0 Reff f i rad i,f u = How long should I wait? i - f 6 1 u = Did something happen before? i 6 1

Consistency of fall-off conditions allowing radiation , local on S2 shift in baseline value of O

S. Pasterski July 30, 2015 4 / 9 Long-time integration at large distances probes low frequencies at the same angle

Radiation Memory – Soft)4 Factor

∂zΦIII

∂zΦII Memory 1 du frad (u) i +

⌘ 1 Massive charges I measure ﬁnite net effect ∂zΦI + R 2 I Radiation I observer anywhere on S u

i 0 1 du... lim Large r observer $ ! 0 - 1 ! I I ex. F.T. takes step function pole R ! i - iq x i!u i!r(1 xˆ qˆ) e · = e · xˆ = qˆ 3 $ d q 1 ↵ ~ iq x I µ(x)=e (2⇡)3 2! ["µ⇤a↵(q)e · + h.c.] A ↵= q ± P R

S. Pasterski July 30, 2015 5 / 9 Radiation Memory – Soft)4 Factor

∂zΦIII

∂zΦII Memory 1 du frad (u) i +

⌘ 1 Massive charges I measure ﬁnite net effect ∂zΦI + R 2 I Radiation I observer anywhere on S u

i 0 1 du... lim Large r observer $ ! 0 - 1 ! I I ex. F.T. takes step function pole R ! i - iq x i!u i!r(1 xˆ qˆ) e · = e · xˆ = qˆ 3 $ d q 1 ↵ ~ iq x I µ(x)=e (2⇡)3 2! ["µ⇤a↵(q)e · + h.c.] A ↵= q ± P R Long-time integration at large distances probes low frequencies at the same angle

S. Pasterski July 30, 2015 5 / 9 Details Soft Factor – Symmetries

null inﬁnity I relevant leading radial behavior of ,g Aµ µ⌫ I ex. Bondi Gauge and BMS as ASG for asymptotically ﬂat spacetimes 2 2 2 mB 2 i ✓ 2 ds = du 2dudr + 2r ¯dzdz¯ + 2 du z = e tan ¯ = zz r 2 zz (1 + zz¯)2  2 z 1 4 1 zz + rCzz dz + D Czz dudz + ( Nz @z (Czz C ))dudz + c.c. + ... r 3 4 I order of limits and stationary phase constraint equations expectation value

S. Pasterski July 30, 2015 6 / 9 Details Soft Factor – Symmetries null inﬁnity constraint equations

I ﬁrst-order in @u e.o.m’s ⌫ 2 ⌫µ = e jµ r F z¯ z 2 ju @uAu = @u(D Az¯ + D Az )+e ju M ) Gµ⌫ = 8⇡GTµ⌫ 1 2 zz 2 z¯z¯ G @umB = @u D C + D C Tuu uu 4 z z¯ ) 3 zz @¯G @ G ¯ Im[@z¯D C ]=⇥ 2Im[@u@z¯Nz +⇤@z¯Tuz ] z uz z uz ) z

I m = 0 scatterers + symmetric in/out radiation + in/out matching -matrix Ward identities )S expectation value

S. Pasterski July 30, 2015 6 / 9 Details Soft Factor – Symmetries null inﬁnity constraint equations expectation value (0) (1) I use soft behavior out a (q) in = S + S out in + (!) h | S| i h |S| i O and constraint equations to get observables⇣ (memory⌘ effects) with:

out : mem : in mem in out h | O S | i hO i| ! ⇠ out in h |S| i I ex. E&M soft factor and mode expansion: (0) p "± µ e + (0)+ S ± = eQ · p = m(1, ~) A = "ˆ⇤ !S p p q z 4⇡ z agree with constraint:· e z + (0)+ z¯ (0) 2 Q 1 lim ![D "ˆz⇤ Sp + D "ˆz⇤¯ Sp ]= e 4⇡ ! 0 4⇡ 2(1 ~ nˆ)2 ! · I When m = 0, view constraint eq. as giving A in terms of free data 6 u A . But A Coulomb ﬁeld, set by in out. z u , ! S. Pasterski July 30, 2015 6 / 9 2 I arbitrary S dependence from boosted monopoles vs. higher multipole of localized static conﬁguration

2 I CFT M on S at of lightcone from origin and 2 ⇢ 4 in/out \ I I Superrotation extension of BMS ASG

I Freedom to Lorentz transform jet directions (RPI) versus angular momentum ﬂux causing observer rotation (Spin Memory)

Applications

BH hair?

M4 holography?

SCET?

S. Pasterski July 30, 2015 7 / 9 Applications

BH hair? 2 I arbitrary S dependence from boosted monopoles vs. higher multipole of localized static conﬁguration

M4 holography? 2 I CFT M on S at of lightcone from origin and 2 ⇢ 4 in/out \ I I Superrotation extension of BMS ASG SCET? I Freedom to Lorentz transform jet directions (RPI) versus angular momentum ﬂux causing observer rotation (Spin Memory)

S. Pasterski July 30, 2015 7 / 9 Spin Memory

Subleading graviton soft factor related to Jµ⌫ µ⌫ (1) pkµ" q Jk⌫ I S = i pk q Xk · I subleading du... vs. du@ ... $ u Superrotation vectorR ﬁelds allowR local CKVs + +z u +z I ⇠ + = Y @z + Dz Y @u + c.c. |I 2 2 I can locally match to different ⇤ near a set of points on the S Spin Memory Effect I chiral observable projects out transitions associated with supertranslations I rotation of geodesic ring, or in ﬁxed-z frame cumulative delay of + 1 z z¯ counterrotating beams: u = du D C dz + D C¯¯dz¯ 2⇡L zz zz Z IC

S. Pasterski July 30, 2015 8 / 9 S. Pasterski July 30, 2015 9 / 9 Black Holes, Holography, and Strings A Celebration of the Science of Andrew Strominger Harvard University Department of Physics July 30 & 31, 2015 www THURSDAY, JULY 30

REGISTRATION AND CONTINENTAL BREAKFAST

8:00 AM REGISTRATION | LYMAN LOBBY CONTINENTAL BREAKFAST | JEFFERSON LIBRARY

9:00 – 9:10 AM WELCOME | JEFFERSON 250 Opening remarks by Stephen Shenker (Stanford)

MORNING LECTURES | JEFFERSON 250

Session Chair: Michael Green (Cambridge) 9:10 – 9:50 AM Bell Inequalities and Cosmological Correlators by Juan Maldacena (IAS) 9:50 – 10:30 AM Chaos in the Black Hole S-Matrix by Joe Polchinski (KITP)

10:30 – 11:00 AM COFFEE BREAK | JEFFERSON LIBRARY

Session Chair: Raphael Bousso (Berkeley) 11:00 – 11:40 PM Black Holes and Moonshine by Jeff Harvey (Chicago) 11:40 – 12:20 PM A Membrane Paradigm at Large D by Shiraz Minwalla (TIFR)

LUNCH

12:20 – 2:20 PM BBQ LUNCH | JEFFERSON COURTYARD

AFTERNOON LECTURES | JEFFERSON 250

Session Chair: Igor Klebanov (Princeton) 2:20 – 3:00 PM Sailing into a Black Hole with Andy by Steve Giddings (UCSB)

3:00 – 3:30 PM COFFEE BREAK | JEFFERSON LIBRARY

3:30 – 5:00 PM STUDENT TALKS | JEFFERSON 250 Session Chair: Hirosi Ooguri (Caltech) TBA by Dionysis Anninos (IAS) Causality and the Conformal Bootstrap A by Thomas Hartman (Cornell) 3D Gravity and String Universality by Alexander Maloney (McGill) Holographic Entanglement for Chern-Simons Terms by Gim Seng Ng (McGill) Dr. Strominger or: How I Learned to Stop Worrying (about singular CKVs) and Love the Triangle by Sabrina Pasterski (Harvard) Supersymmetry Constraints on String Dynamics by Xi Yin (Harvard)

EVENING BANQUET | KNAFEL CENTER, 10 GARDEN ST.

6:30 – 10:00 PM COCKTAIL RECEPTION AND BANQUET: Dress Code: ‘Physics casual’ Black Holes, Holography, and Strings A Celebration of the Science of Andrew Strominger Harvard University Department of Physics July 30 & 31, 2015 www

FRIDAY, JULY 31

CONTINENTAL BREAKFAST

8:00 AM CONTINENTAL BREAKFAST | JEFFERSON LIBRARY

MORNING LECTURES | JEFFERSON 250

Session Chair: David Morrison (UC Santa Barbara) 9:00 – 9:40 AM F-theory and 5d Spinning Black Holes by Cumrun Vafa (Harvard) 9:40 – 10:20 AM Measuring the Elliptic Genus by Greg Moore (Rutgers)

10:20 – 10:50 AM COFFEE BREAK | JEFFERSON LIBRARY

Session Chair: Herman Verlinde (Princeton) 10:50 – 11:30 AM Anomalies, Conformal Manifolds, and Spheres by Nathan Seiberg (IAS) 11:30 – 12:10 PM Gravity Dual of Information Metric by Tadashi Takayanagi (Kyoto & IPMU)

LUNCH

12:10 – 2:00 PM BUFFET LUNCH | JEFFERSON LIBRARY

AFTERNOON LECTURES | JEFFERSON 250

Session Chair: Erik Verlinde (Amsterdam) 2:00 – 2:40 PM The Higher Spin Square by Rajesh Gopakumar (ICTS Bangalore) 2:40 – 3:20 PM Towards Emergent Time by Nima Arkani-Hamed (IAS)

3:20 – 3:50 PM COFFEE BREAK | JEFFERSON LIBRARY

Session Chair: Robbert Dijkgraff (IAS) 3:50 – 4:30 PM Fun with Fermions by Frederik Denef (Columbia) 4:30 – 5:10 PM An Extremal Black Hole Surprise by Gary Horowitz (UCSB)

Additional Information

Extra Collaboration Space: Jefferson 453 and HETG Lounge Late Registrations: Jefferson 453

Wireless Networks: “eduroam” or “Harvard Guest”

Useful Phone Numbers: Cambridge Taxi Cab (617) 649-7000 Cambridge Taxi (617) 718 - 4000