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Causality Constraints in Quantum Field Theory and Quantum Gravity

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Causality Constraints in Quantum Field Theory and Quantum Gravity CAUSALITY CONSTRAINTS IN QUANTUM FIELD THEORY AND QUANTUM GRAVITY A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Nima Afkhami-Jeddi August 2019 c 2019 Nima Afkhami-Jeddi ALL RIGHTS RESERVED CAUSALITY CONSTRAINTS IN QUANTUM FIELD THEORY AND QUANTUM GRAVITY Nima Afkhami-Jeddi, Ph.D. Cornell University 2019 We explore the consequences of micro-causality in quantum field theory and quan- tum gravity. To this end, we develop methods in conformal field theories (CFT) by considering collider type experiments. Using this, we find a class of positive operators in a certain class of holographic CFTs. Positivity of these operators helps to describe the mechanism for the emergence of weakly interacting Einstein gravity description of the dual theory in anti de-Sitter spacetime. We also pro- vide a dictionary for describing how these operators play a role in the dual bulk spacetime as shockwave states. Furthermore, we develop techniques to explore the consequences of causality in flat spacetimes by studying S-matrix consistency conditions. Using these methods, we place constraints on the higher spin spectrum of theories that include gravitational interactions. BIOGRAPHICAL SKETCH Nima Afkhami-Jeddi was born on Feb 14 1987 in Tehran, Iran. He moved to Toronto, Canada with his family in 2001. After high-school he briefly attended Centennial College and worked as a licenced automechanic. He then attended York University starting in 2008 majoring in biochemistry to pursue a career in the medical field. He changed career paths by switching his study major to physics and working in the atomic physics laboratory of A. Kumarakrishnan at York Uni- versity. He then attended Perimeter Institute for Theoretical Physics starting in 2013 as a student in the M.Sc. program, completing his thesis under the super- vision of Freddy Cachazo. Upon completion he joined Tom Hartman's group at Cornell University in 2014 resulting in this dissertation among other works. He will continue his research as a post-doctoral fellow at the Kadanoff Institute at the University of Chicago. iii Dedicated to Fjolla and my family, Thank you. iv ACKNOWLEDGEMENTS The past five years at Cornell have been the most intellectually fulfilling period of my life so far. This would not have been possible without the guidance and support of many people with whom I have interacted throughout the years. First and foremost I am immeasurably grateful to my advisor Tom Hartman who has been an exceptional mentor and for his patience in guiding me through the complexities of research. His dedication, professionalism, and clarity of thought are an inspiration for me. I have no doubts that his teachings will provide me with a strong stepping stone on my path towards research. I would also like to thank Liam McAllister for his guidance through various stages of my academic growth as a graduate student, for sharing his knowledge with me through many interesting discussions, and for his teachings. I am grateful to my teachers at Cornell including Csaba Csaki, Yuval Grossman, Peter Lepage for sharing their knowledge with me. I owe a deep debt of gratitude to my collaborators without whom this work would not have been possible. I would like to thank Amirhossein Tajdini and Sandipan Kundu who have been my collaborators on a large part of the work that have resulted in this thesis. I would also like to thank Alexander Maloney, Kale Colville and Eric Perlmutter who have been my collaborators on other projects. I would like to thank John Stout, Cody Long, Sachin Jain, Sungwoo Hong, Edgar Shaghoulian, Mudassir Moosa, Ibrahim Shehzad, Mehmet Demirtas and Gowri Kurup who are students and postdocs for many interesting discussions and for their friendship. They have no doubt contributed greatly to my education and to my well-being during my time in Ithaca. Finally, I would like to thank the physics community at Cornell for making this great experience possible. v TABLE OF CONTENTS Biographical Sketch . iii Dedication . iv Acknowledgements . .v Table of Contents . vi List of Figures . ix 1 Introduction1 2 Shockwaves from the Operator Product Expansion6 2.1 Introduction . .7 2.1.1 Shockwaves from heavy operators . 10 2.1.2 Shockwaves from light operators . 11 2.1.3 Causality constraints . 13 2.2 Shockwaves from Heavy Operators . 14 2.2.1 Shockwave solutions in AdS . 16 2.2.2 Shockwave states in CFT . 19 2.3 The Regge OPE . 24 2.3.1 The length operator . 26 2.3.2 CFT interpretation . 30 2.4 Causality constraints revisited . 35 2.4.1 The Engelhardt-Fischetti criterion . 35 2.4.2 Time delays for probe particles . 38 2.5 Shockwaves from light operators . 45 2.5.1 Smeared operators . 46 2.5.2 Shockwaves in the smeared OPE . 49 2.5.3 Gravity derivation . 50 2.5.4 CFT derivation from conformal Regge theory . 51 2.6 Smearing operators with spin . 55 2.6.1 Setup . 56 2.6.2 JJ .............................. 57 2.6.3 T T .............................. 59 3 A Conformal Collider for Holographic CFTs 61 3.1 Introduction . 62 3.2 Causality and conformal collider physics . 71 3.2.1 A collider for holographic CFTs . 72 3.2.2 Holographic null energy condition . 74 3.2.3 Corrections from higher spin operators . 82 3.3 Universality of the smeared Regge OPE . 84 3.3.1 Gravity interpretation . 87 vi 3.4 Nitty-gritty of doing the integrals . 89 3.4.1 Scalar operators . 91 3.4.2 Spinning operators . 96 3.5 Bounds on TTT , JJT , and `=1;2 `=1;2T ........... 98 3.5.1 JJTh ..............................i h i hO O i 98 3.5.2 hTTTi .............................. 100 3.5.3 h i T .......................... 103 hO`=1O`=1 i 3.5.4 `=2 `=2T .......................... 105 3.6 BoundshO fromO interferencei effect . 107 3.7 Constraints on CFTs in D =3..................... 112 3.7.1 TTT .............................. 112 3.7.2 hJJT i .............................. 115 3.7.3 hT T i .............................. 115 3.8 Constrainingh i inflationary observables . 117 3.8.1 Chiral gravity waves . 118 3.8.2 Tensor-to-scalar ratio . 119 3.8.3 Graviton non-gaussanity . 120 3.9 Discussion . 121 4 A Bound on Massive Higher Spin Particles 125 4.1 Introduction . 126 4.2 Higher Spin Fields in Flat Spacetime . 133 4.2.1 Eikonal Scattering . 136 4.2.2 Higher Spin-graviton Couplings . 139 4.2.3 Eikonal Kinematics . 142 4.2.4 Bounds on Coefficients . 145 4.2.5 D =4 .............................. 149 4.2.6 Comments . 154 4.3 Higher Spin Fields in AdSD ...................... 159 4.3.1 Causality and Conformal Regge Theory . 161 4.3.2 D > 4 .............................. 167 4.3.3 AdS4/CFT3 ........................... 174 4.3.4 Maldacena-Zhiboedov Theorem and Massless Higher Spin Fields . 176 4.3.5 Comments . 179 4.4 Restoring Causality . 182 4.4.1 Make CFT Causal Again . 182 4.4.2 Stringy Operators above the Gap . 185 4.5 Cosmological Implications . 189 vii A Appendices 193 A.1 Witten diagram calculations . 193 A.1.1 Feynman rules . 193 A.1.2 Vertex diagram . 195 A.1.3 4-point functions . 197 A.2 Check of the stress-tensor block . 198 A.2.1 Time delay from the Dolan-Osborn block . 200 A.3 Derivation of the general Lightcone and Regge block . 200 A.4 Smearing the Regge amplitude . 202 A.5 Regge amplitude for JJ ..................... 203 A.6 Three-point functionsh of conservedi currents . 205 A.6.1 JJT .............................. 205 A.6.2 hTTTi .............................. 206 A.7 Three-pointh functionsi in D =3 .................... 208 A.7.1 JJT .............................. 208 A.7.2 hTTTi .............................. 209 A.8 d-dimensionalh i smearing integrals . 209 A.9 Polarization vectors . 210 A.10 Transverse Polarizations . 214 A.11 Phase Shift Computations . 215 A.12 Parity Violating Interactions in D =5 ................ 220 A.13 Correlators of Higher Spin Operators in CFT . 222 A.14 Details of Spin-3 Calculation in D > 4 ................ 224 A.15 Details of Spin-4 Calculation in D > 4 ................ 230 A.16 Details of CFT3 calculations . 234 Bibliography 237 viii LIST OF FIGURES 2.1 Planar shockwave (2.2.1) in Poincare coordinates . .8 2.2 Spherical shockwave (2.2.7) in Poincare coordinates . .9 2.3 Shockwave in global AdS . 15 2.4 Boundary version of figure 2.3..................... 22 2.5 The Regge limit of operator product (u; v) ( u; v)....... 25 2.6 Setup for the four-point function . .− . .− . 40 2.7 The smearing region on the z andz ¯ ................. 48 3.1 Conformal collider experiment . 71 3.2 Graviton contribution to the Regge OPE . 75 3.3 Kinematics for the holographic null energy condition . 77 3.4 The Witten diagram for graviton in Regge OPE . 79 4.1 Spectrum of higher spin particles . 131 4.2 The building blocks of ladder diagrams. 134 4.3 Eikonal scattering of particles . 135 4.4 The three-point interaction of graviton with higher spin particles . 140 4.5 Bounds from interference in D =4.................. 152 4.6 Holographic null energy condition (HNEC) . 167 4.7 The squeezed limit of three-point functions. 190 ix CHAPTER 1 INTRODUCTION Quantum field theories are arguably the most successful framework for de- scribing many physical phenomena observed in nature ranging over orders of mag- nitudes in scale from high energy particle physics at particle accelerators to the behavior of low energy condensed matter systems. According to the modern per- spective, the space of QFTs can be understood as the space of renormalization group flows describing the dynamics from high energy scales in the UV to the low energy scales in the IR.
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