Aspects of Symmetry in the Infrared The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Pate, Monica Ichiye. 2019. Aspects of Symmetry in the Infrared. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:42106945 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Aspects of Symmetry in the Infrared a dissertation presented by Monica Ichiye Pate to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts May 2019 ©2019 – Monica Ichiye Pate all rights reserved. Thesis advisor: Professor Andrew Strominger Monica Ichiye Pate Aspects of Symmetry in the Infrared Abstract This dissertation studies a class of infinite-dimensional symmetries, known as asymptotic symme- tries, across a variety of gauge and gravitational theories. In identifying the physical implications of these symmetries with other well-known infrared phenomena, a precise equivalence is established among soft theorems, memory effects and asymptotic symmetries, called the infrared triangle. In U(1) gauge theories with only massless charged particles, the soft photon theorem was previously identified as the Wardidentity of an infinite-dimensional asymptotic symmetry group. The symmetry group comprises of gauge transformations which approach angle-dependent constants at null infinity. Here, the analysis is extended to all U(1) theories, including those with massive charged particles such as QED. Next, implications of the U(1) large gauge symmetry for a holographic dual are considered. The soft factorization theorem for 4D abelian gauge theory is shown to be mathematically equivalent to the factorization of correlation functions on the sphere in a 2D CFT with a U(1) Kac-Moody current alge- bra. The soft ‘t Hooft-Wilson lines and soft photons are realized as a complexified 2D current algebra on the celestial sphere at null infinity with the level determined by the cusp anomalous dimension. Then, a universal gravitational memory effect, measurable by inertial detectors, is established in even spacetime dimensions d > 4. The effect exhibits (3 − d)th power law fall-off behavior at large iii Thesis advisor: Professor Andrew Strominger Monica Ichiye Pate radius r and belongs to an infrared triangle that includes Weinberg’ssoft graviton theorem and infinite- dimensional asymptotic symmetries. In the final part of this dissertation, color memory - the non-abelian gauge theoretic analog of the gravitational memory effect - is determined. A formula for the net relative SU(3) color rotation of a pair of nearby quarks that is induced by the transit of color radiation is derived from conservation laws for large gauge symmetry in non-abelian gauge theories. For weak color flux, it linearizes to the Fourier transform of the soft gluon theorem. It is proposed that this effect can be measured in the Regge limit of deeply inelastic scattering at electron-ion colliders. iv Contents Title Page ......................................... i Abstract .......................................... iii Table of Contents ..................................... v Citations to Previously Published Work . vii Dedication ........................................ viii Acknowledgments .................................... ix 1 Introduction and Summary 1 1.1 Asymptotic symmetries .............................. 2 1.2 The infrared triangle ................................ 4 1.3 Evidence for universality .............................. 6 2 New Symmetries of QED 10 2.1 Introduction .................................... 10 2.2 Abelian gauge theory with massive matter ..................... 12 2.3 Symmetries of the S-matrix ............................ 20 3 Soft Factorization in QED from 2D Kac-Moody Symmetry 28 3.1 Introduction .................................... 28 3.2 Abelian gauge theory in hyperbolic coordinates . 31 3.3 Soft photon current algebra ............................ 33 3.4 Boundary gauge modes ............................... 37 3.5 Soft Wilson lines .................................. 39 3.6 Magnetic charges .................................. 44 3.7 Non-perturbative soft S-matrix .......................... 51 3.8 Soft factorization .................................. 53 4 Gravitational Memory in Higher Dimensions 55 4.1 Introduction .................................... 55 4.2 General relativity in d = 2m + 2 > 4 ....................... 57 4.3 Gravitational memory in d = 6 .......................... 63 4.4 Weinberg’s soft theorem in d = 6 .......................... 66 4.5 Higher dimensional generalization ......................... 74 v 5 Color Memory 82 5.1 Introduction .................................... 82 5.2 Yang-Mills theory .................................. 85 5.3 Color memory effect ................................ 88 6 Measuring Color Memory in a Color Glass Condensate at Electron- Ion Colliders 93 6.1 Introduction .................................... 93 6.2 Brief review of color memory ............................ 97 6.3 Color memory in the CGC ............................. 101 6.4 Measuring color memory in deeply inelastic scattering . 111 7 Conclusion 121 Appendix A Appendix to Chapter 2 125 A.1 Gauge field strength near i0 ............................. 125 Appendix B Appendix to Chapter 4 128 B.1 Asymptotic expansions ............................... 128 B.2 Residual gauge-fixing ................................ 130 B.3 Canonical charges ................................. 136 Appendix C Appendix to chapter 6 139 C.1 Classical colored particles .............................. 139 References 153 vi Citations to Previously Published Work Much of the material in this dissertation has been previously published in papers. The relevant cita- tions are listed below: The content of chapter 2 has appeared in the paper: “New Symmetries of QED,” D. Kapec, M. Pate and A. Strominger, Adv. Theor. Math. Phys. 21, 1769 (2017), hep-th/1506.02906. The content of chapter 3 has appeared in the paper: “Soft Factorization in QED from 2D Kac-Moody Symmetry,” A. Nande, M. Pate and A. Stro- minger, JHEP 1802, 079 (2018), hep-th/1705.00608. The content of chapter 4 has appeared in the paper: “Gravitational Memory in Higher Dimensions,” M. Pate, A. M. Raclariu and A. Strominger, JHEP 1806, 138 (2018), hep-th/1712.01204. The content of chapter 5 has appeared in the paper: “Color Memory: A Yang-MillsAnalog of Gravitational Wave Memory,” M. Pate, A. M. Raclariu and A. Strominger, Phys. Rev. Lett. 119, no. 26, 261602 (2017), hep-th/1707.08016. The content of chapter 6 has appeared in the arXiv preprint: “Measuring Color Memory in a Color Glass Condensate at Electron-Ion Colliders,” A. Ball, M. Pate, A. M. Raclariu, A. Strominger and R. Venugopalan, hep-ph/1805.12224. Electronic preprints (shown in typewriter font) are available on the internet at the following URL: http://arXiv.org vii Tomy mother for teaching me perseverance, Tomy father for encouraging me to dream, And to my sister, for inspiring me, by example, to be brave. viii Acknowledgments I am deeply grateful to Andy Strominger for his continual guidance and encouragement through- out my graduate studies. It has been a privilege and an honor to work for an advisor who has both the curiosity and insight of a true scholar, while at the same time remains warm, welcoming and patient. In addition, it through his efforts that the strings group at Harvard continues to be a strings family.I am grateful to him for sustaining this vibrant and nurturing community, in which young physicists can develop and thrive. I am also very grateful to Raju Venugopalan for patiently explaining to me subtle aspects of QCD and providing me with numerous opportunities to interact with experts in the field. In addition, I am especially thankful to Ana Raclariu, both a fantastic friend and physicist, who made the numer- ous projects on which we collaborated truly wonderful experiences. It goes without saying that I am grateful to all of my other coauthors, including Adam Ball, Dan Kapec, and Anjalika Nande. One of the great joys in science is discussing the ideas you uncover, whether they are new or known, with people who share a common interest and understanding of the field. As such, I would like to thank various past and present members of the high-energy theory group at Harvard including Nathan Agmon, Anders Andreassen, Agnese Bissi, Bruno Balthazar, Laura Donnay, Chris Frye, Delilah Gates, Shahar Hadar, Daniel Harlow, Hofie Hannesdottir, Mina Himwich, Monica Kang, David Kolch- meyer, Sruthi Narayanan, Sabrina Pasterski, Abhishek Pathak, Achilleas Porfyriadis, Andrea Puhm, ix Victor Rodriguez, Shu-Heng Shao and Lily Shi. I am grateful to Daniel Jafferis and Cumrum Vafa for sharing their knowledge with me and especially to Xi Yin for bringing me (as a beginning graduate student) up to speed as fast as possible. I would like to thank Temple He, Alex Lupsasca, and Prahar Mitra for whole-heartedly embracing the role of “older academic sibling” and helping me prepare for what was to come. At frustrating moments in graduate school, I have benefitted greatly from a fresh perspective. I want to thank James