Lectures on the Infrared Structure of Gravity and Gauge Theory
Description
Lectures on the Infrared Structure of Gravity and Gauge Theory presents an accessible, graduate-level synthesis of a frontier research area in theoretical physics. Based on a popular Harvard University course taught by the author, this book gives a concise introduction to recent discoveries concerning the structure of gravity and gauge theory at very long distances. These discoveries unite three disparate but well-developed subjects in physics.
The first subject is the soft theorems, which were found by particle physicists in the 1950s to control the behavior of low-energy photons and are essential for all collider predictions. The second subject is asymptotic symmetries, found by general relativists in the 1960s to provide a surprising, infinite number of exact relations between distinct physical phenomena. The third subject is the memory effect, the measurement of which is sought in upcoming gravitational wave observations. An exploration of the physical and mathematical equivalence of these three subjects has provided a powerful new perspective on old results and led to a plethora of new results, involving symmetries of QED, gluon scattering amplitudes, flat-space holography in quantum gravity, black hole information, and beyond.
Uniquely connective and cutting-edge, Lectures on the Infrared Structure of Gravity and Gauge Theory takes students and scholars to the forefront of new developments in the discipline.
- Materials are presented in a "lecture notes" style with problem sets included
- Concise and accessible pedagogical approach
- Topics include soft theorems, the memory effect, asymptotic symmetries with applications to QED, Yang-Mills theory, quantum gravity, and black holes
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Content
Preface xi 1. Introduction 1 1.1 The Infrared Triangle 1 1.2 New Developments 3 1.3 Echoing Triangles 4 1.3.1 QED, Yang-Mills Theory, Gravity, Massless Particles, . . . 4 1.3.2 Leading, Subleading, Sub-Subleading, . . . 5 1.3.3 Double Soft Theorems, . . . 6 1.3.4 Classical, quantum, . . . 6 1.3.5 Minkowski , D < 4, D > 4, Cosmology, . . . 6 1.3.6 Supersymmetry, N = 1, 2, . . . 6 1.4 Motivation and Applications 7 1.4.1 Connecting Disparate Subjects 7 1.4.2 Flat Space Holography 7 1.4.3 The Gauge Theory S-Matrix 8 1.4.4 Miracles in N = 4 Yang-Mills 8 1.4.5 Black Holes 9 2. QED 10 2.1 Liénard-Wiechert Solution 11 2.2 Minkowski Space Penrose Diagram 12 2.3 Antipodal Matching Condition 15 2.4 Asymptotic Expansions 18 2.5 An Infinity of Conserved Charges 20 2.6 Canonical Electrodynamics at I 24 2.6.1 Symplectic Form 25 2.6.2 Commutators 26 2.7 Large Gauge Symmetry 27 2.8 Ward Identity 28 2.8.1 Symmetries of the S-Matrix 29 2.8.2 Mode Expansions 30 2.8.3 Soft Theorems 33 2.9 Feynman Diagrammatics 34 2.9.1 Soft Photons 34 2.9.2 Soft Gravitons 37 2.10 Asymptotic Symmetries 38 2.11 Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons 41 2.12 Massive QED 45 2.12.1 Hyperbolic Slices 47 2.12.2 Soft Theorem 49 2.13 Magnetic Charges 51 2.14 Supersymmetry 54 2.14.1 Soft Photino Theorem 55 2.14.2 Fermionic Conservation Laws 56 2.14.3 N = 4, 8 59 2.15 Infrared Divergences 59 3. The S-Matrix as a Celestial Correlator 64 4. Nonabelian Gauge Theory 67 4.1 G-Kac-Moody Algebra 68 4.2 Conserved Charges 72 5. Gravity 73 5.1 Asymptotically Flat Spacetimes 73 5.2 Supertranslations 75 5.2.1 BMS Analysis 75 5.2.2 The Scattering Problem 80 5.2.3 Conserved Charges 80 5.3 Superrotations 82 5.3.1 Conserved Charges 82 5.3.2 Symmetries 83 5.3.3 Canonical Formalism 86 5.3.4 Subleading Soft Theorem 87 6. The Memory Effect 90 7. Black Holes 95 7.1 The Information Paradox 95 7.2 Soft Hair 99 7.2.1 Classical Hair 101 7.2.2 Horizon Charges 105 7.2.3 Quantum Hair 107 7.2.4 Electric Hair 107 7.3 Discussion 113 Exercises with Prahar Mitra and Monica Pate 117 Solutions with Prahar Mitra and Monica Pate 127 References 169 Index 181
