Lectures on the Infrared Structure of Gravity and Gauge Theory

199 Pages·2018·3.554 MB·English

by  Andrew Strominger

Lectures on the Infrared Structure
of Gravity and Gauge Theory

Lectures on the Infrared Structure
of Gravity and Gauge Theory
ANDREW STROMINGER
PRINCETON UNIVERSITY PRESS
PrincetonandOxford
Copyright(cid:2)c 2018byPrincetonUniversityPress
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Contents
Preface xi
1. Introduction 1
1.1 TheInfraredTriangle 1
1.2 NewDevelopments 3
1.3 EchoingTriangles 4
1.3.1 QED,Yang-MillsTheory,Gravity,MasslessParticles,... 4
1.3.2 Leading,Subleading,Sub-Subleading,... 5
1.3.3 DoubleSoftTheorems,... 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 MotivationandApplications 7
1.4.1 ConnectingDisparateSubjects 7
1.4.2 FlatSpaceHolography 7
1.4.3 TheGaugeTheoryS-Matrix 8
1.4.4 MiraclesinN =4Yang-Mills 8
1.4.5 BlackHoles 9
2. QED 10
2.1 Liénard-WiechertSolution 11
2.2 MinkowskiSpacePenroseDiagram 12
2.3 AntipodalMatchingCondition 15
2.4 AsymptoticExpansions 18
2.5 AnInfinityofConservedCharges 20
2.6 CanonicalElectrodynamicsatI 24
2.6.1 SymplecticForm 25
2.6.2 Commutators 26
2.7 LargeGaugeSymmetry 27
2.8 WardIdentity 28
2.8.1 SymmetriesoftheS-Matrix 29
2.8.2 ModeExpansions 30
2.8.3 SoftTheorems 33
2.9 FeynmanDiagrammatics 34
viii CONTENTS
2.9.1 SoftPhotons 34
2.9.2 SoftGravitons 37
2.10 AsymptoticSymmetries 38
2.11 SpontaneousSymmetryBreaking,VacuumDegeneracy,and
GoldstoneBosons 41
2.12 MassiveQED 45
2.12.1 HyperbolicSlices 47
2.12.2 SoftTheorem 49
2.13 MagneticCharges 51
2.14 Supersymmetry 54
2.14.1 SoftPhotinoTheorem 55
2.14.2 FermionicConservationLaws 56
2.14.3 N =4,8 59
2.15 InfraredDivergences 59
3. TheS-MatrixasaCelestialCorrelator 64
4. NonabelianGaugeTheory 67
4.1 G-Kac-MoodyAlgebra 68
4.2 ConservedCharges 72
5. Gravity 73
5.1 AsymptoticallyFlatSpacetimes 73
5.2 Supertranslations 75
5.2.1 BMSAnalysis 75
5.2.2 TheScatteringProblem 80
5.2.3 ConservedCharges 80
5.3 Superrotations 82
5.3.1 ConservedCharges 82
5.3.2 Symmetries 83
5.3.3 CanonicalFormalism 86
5.3.4 SubleadingSoftTheorem 87
6. TheMemoryEffect 90
7. BlackHoles 95
7.1 TheInformationParadox 95
7.2 SoftHair 99
7.2.1 ClassicalHair 101
7.2.2 HorizonCharges 105
7.2.3 QuantumHair 107
CONTENTS ix
7.2.4 ElectricHair 107
7.3 Discussion 113
ExerciseswithPraharMitraandMonicaPate 117
SolutionswithPraharMitraandMonicaPate 127
References 169
Index 181