Supersymmetry and String Theory: Beyond the Standard Model

504 Pages·2016·2.104 MB·English

by  Michael Dine

SupersymmetryandStringTheory
BeyondtheStandardModel
The past decade has witnessed dramatic developments in the fields of experimental and
theoretical particle physics and cosmology. This Second Edition is a comprehensive
introduction to these recent developments and brings this self-contained textbook right
up to date. Brand-new material for this edition includes the ground-breaking Higgs
discovery and results of the WMAP and Planck experiments. Extensive discussion
of theories of dynamical electroweak symmetry breaking, metastable supersymmetry
breaking,anexpandeddiscussionofinflationandanewchapteronthelandscape,aswell
as a completely rewritten coda on future directions, give readers a modern perspective
on this developing field. A focus on three principal areas – supersymmetry, string
theory and astrophysics and cosmology – provides the structure for this book, which
will be of great interest to graduates and researchers in the fields of particle theory,
string theory, astrophysics and cosmology. The book contains several problems, and
password-protected solutions will be available to lecturers at www.cambridge.org/
9781107048386.
MichaelDine is Professor of Physics at the University of California, Santa Cruz. He is an
A.P.SloanFoundationFellow,aFellowoftheAmericanPhysicalSocietyandaFellowof
theAmericanAcademyofArtsandSciences.Priortothis,ProfessorDinewasaResearch
Associateat theStanford Linear Accelerator Center, along-termmember of theInstitute
forAdvancedStudyandHenrySematProfessorattheCityCollegeoftheCityUniversity
ofNewYork.
Reviewsofthefirstedition
“Anexcellentandtimelyintroductiontoawiderangeoftopicsconcerningphysicsbeyond
the standard model, by one of the most dynamic researchers in the field. Dine has a gift
forexplainingdifficultconceptsinatransparentway.Thebookhaswonderfulinsightsto
offerbeginninggraduatestudentsandexperiencedresearchersalike.”
NimaArkani-Hamed,HarvardUniversity
“How many times did you need to find the answer to a basic question about the
formalism and especially the phenomenology of general relativity, the Standard Model,
itssupersymmetricandgrandunifiedextensions,andotherseriousmodelsofnewphysics,
aswellasthemostimportantexperimentalconstraintsandtherealizationofthekeymodels
withinstringtheory?Dine’sbookwillsolvemostoftheseproblemsforyouandgiveyou
muchmore,namelythestate-of-the-artpictureofrealityasseenbyaleadingsuperstring
phenomenologist.”
LubosMotl,HarvardUniversity
“Thisbookgivesabroadoverviewofmostofthecurrentissuesintheoreticalhighenergy
physics.Itintroducesanddiscussesawiderangeoftopicsfromapragmaticpointofview.
Although some of these topics are addressed in other books, this one gives a uniform
and self-contained exposition of all of them. The book can be used as an excellent text
in various advanced graduate courses. It is also an extremely useful reference book for
researchers in the field, both for graduate students and established senior faculty. Dine’s
deep insights and broad perspective make this book an essential text. I am sure it will
become a classic. Many physicists expect that with the advent of the LHC a revival of
modelbuildingwilltakeplace.Thisbookisthebesttoolkitamodernmodelbuilderwill
need.”
NathanSeiberg,InstituteforAdvancedStudy,Princeton
Supersymmetry and String
Theory, Second Edition
Beyond the Standard Model
MICHAEL DINE
UniversityofCalifornia,SantaCruz
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Firstpublished2015
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Dine,Michael,author.
Supersymmetryandstringtheory:beyondthestandardmodel/MichaelDine,
UniversityofCalifornia,
SantaCruz.–Secondedition.
pages cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-107-04838-6(Hardback)
1. Supersymmetry. 2. Stringmodels. I. Title.
QC174.17.S9D56 2015
(cid:2)
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ThisbookisdedicatedtoMarkandEstherDine

Contents
PrefacetotheFirstEdition pagexv
PrefacetotheSecondEdition xviii
Anoteonthechoiceofmetric xx
Textwebsite xxi
Part1 Effectivefieldtheory:theStandardModel,supersymmetry,
unification 1
1 BeforetheStandardModel 3
Suggestedreading 7
2 TheStandardModel 8
2.1 Yang–Millstheory 8
2.2 Realizationsofsymmetryinquantumfieldtheory 10
2.3 ThequantizationofYang–Millstheories 16
2.4 TheparticlesandfieldsoftheStandardModel:gaugebosonsandfermions 20
2.5 TheparticlesandfieldsoftheStandardModel:Higgsscalarsandthe
completeStandardModel 22
2.6 Thegaugebosonmasses 23
2.7 Quarkandleptonmasses 24
2.8 TheHiggsfieldanditscouplings 25
Suggestedreading 26
Exercises 26
3 PhenomenologyoftheStandardModel 27
3.1 Theweakinteractions 27
3.2 DiscoveryoftheHiggs 29
3.3 Thequarkandleptonmassmatrices 32
3.4 Thestronginteractions 34
3.5 Therenormalizationgroup 36
3.6 Calculatingthebetafunction 39
3.7 Thestronginteractionsanddimensionaltransmutation 43
3.8 Confinementandlatticegaugetheory 44
3.9 Stronginteractionprocessesathighmomentumtransfer 51
Suggestedreading 61
Exercises 62
vii
viii Contents
4 TheStandardModelasaneffectivefieldtheory 63
4.1 Integratingoutmassivefields 63
4.2 Leptonandbaryonnumberviolation;neutrinomass 67
4.3 ChallengesfortheStandardModel 71
4.4 Thenaturalnessprinciple 74
4.5 Summary:successesandlimitationsoftheStandardModel 75
Suggestedreading 75
5 Anomalies,instantonsandthestrongCPproblem 76
5.1 Thechiralanomaly 77
5.2 Atwo-dimensionaldetour 81
5.3 RealQCD 88
5.4 ThestrongCPproblem 98
5.5 PossiblesolutionsofthestrongCPproblem 100
Suggestedreading 104
Exercises 104
6 Grandunification 106
6.1 Cancelationofanomalies 108
6.2 Renormalizationofcouplings 108
6.3 BreakingtoSU(3)×SU(2)×U(1) 109
6.4 SU(2)×U(1)breaking 110
6.5 Chargequantizationandmagneticmonopoles 111
6.6 Protondecay 112
6.7 Othergroups 112
Suggestedreading 114
Exercises 115
7 Magneticmonopolesandsolitons 116
7.1 Solitonsin1+1dimensions 117
7.2 Solitonsin2+1dimensions:stringsorvortices 118
7.3 Magneticmonopoles 119
7.4 TheBPSlimit 120
7.5 Collectivecoordinatesforthemonopolesolution 122
7.6 TheWitteneffect:theelectricchargeinthepresenceofθ 123
7.7 Electric–magneticduality 124
Suggestedreading 125
Exercises 125
8 Technicolor:afirstattempttoexplainhierarchies 126
8.1 QCDinaworldwithoutHiggsfields 127
8.2 Fermionmasses:extendedtechnicolor 128
8.3 TheHiggsdiscoveryandprecisionelectroweakmeasurements 130
8.4 TheHiggsasaGoldstoneparticle 131
ix Contents
Suggestedreading 131
Exercises 132
Part2 Supersymmetry 133
9 Supersymmetry 135
9.1 Thesupersymmetryalgebraanditsrepresentations 136
9.2 Superspace 136
9.3 N=1Lagrangians 140
9.4 Thesupersymmetrycurrents 142
9.5 Thegroundstateenergyingloballysupersymmetrictheories 143
9.6 Somesimplemodels 144
9.7 Non-renormalizationtheorems 146
9.8 Localsupersymmetry:supergravity 148
Suggestedreading 149
Exercises 150
10 Afirstlookatsupersymmetrybreaking 151
10.1 Spontaneoussupersymmetrybreaking 151
10.2 Thegoldstinotheorem 153
10.3 Loopcorrectionsandthevacuumdegeneracy 154
10.4 Explicitsoftsupersymmetrybreaking 155
10.5 Supersymmetrybreakinginsupergravitymodels 157
Suggestedreading 159
Exercises 159
11 TheMinimalSupersymmetricStandardModel 160
11.1 SoftsupersymmetrybreakingintheMSSM 162
11.2 SU(2)×U(1)breaking 166
11.3 EmbeddingtheMSSMinsupergravity 167
11.4 RadiativecorrectionstotheHiggsmasslimit 168
11.5 FinetuningoftheHiggsmass 170
11.6 Reducingthetuning:theNMSSM 170
11.7 Constraints on low-energy supersymmetry: direct searches and rare
processes 171
Suggestedreading 176
Exercises 176
12 Supersymmetricgrandunification 177
12.1 Asupersymmetricgrandunifiedmodel 177
12.2 Couplingconstantunification 178
12.3 Dimension-fiveoperatorsandprotondecay 179
Suggestedreading 181
Exercises 181
x Contents
13 Supersymmetricdynamics 182
13.1 Criteriaforsupersymmetrybreaking:theWittenindex 182
13.2 Gauginocondensationinpuregaugetheories 184
13.3 SupersymmetricQCD 185
13.4 N <N:anon-perturbativesuperpotential 188
f
13.5 ThesuperpotentialinthecaseN <N−1 190
f
13.6 N =N−1:theinstanton-generatedsuperpotential 191
f
Suggestedreading 196
Exercises 196
14 Dynamicalsupersymmetrybreaking 198
14.1 Modelsofdynamicalsupersymmetrybreaking 198
14.2 Metastablesupersymmetrybreaking 200
14.3 Particlephysicsanddynamicalsupersymmetrybreaking 203
Suggestedreading 209
Exercises 210
15 Theorieswithmorethanfourconservedsupercharges 211
15.1 N=2theories:exactmodulispaces 211
15.2 Astillsimplertheory:N=4Yang–Mills 213
15.3 AdeeperunderstandingoftheBPScondition 214
15.4 Seiberg–Wittentheory 216
Suggestedreading 221
Exercises 221
16 Moresupersymmetricdynamics 222
16.1 Conformallyinvariantfieldtheories 222
16.2 MoresupersymmetricQCD 224
16.3 N =N 224
f c
16.4 N >N+1 228
f
16.5 N ≥3N/2 229
f
Suggestedreading 229
Exercises 230
17 Anintroductiontogeneralrelativity 231
17.1 Tensorsingeneralrelativity 232
17.2 Curvature 236
17.3 Thegravitationalaction 237
17.4 TheSchwarzschildsolution 239
17.5 FeaturesoftheSchwarzschildmetric 241
17.6 Couplingspinorstogravity 243
Suggestedreading 244
Exercises 244