This page intentionally left blank SUPERSYMMETRY AND STRING THEORY Beyond the Standard Model The past decade has witnessed some dramatic developments in the field of theoret- ical physics, including advancements in supersymmetry and string theory. There have also been spectacular discoveries in astrophysics and cosmology. The next few years will be an exciting time in particle physics with the start of the Large Hadron Collider at CERN. This book is a comprehensive introduction to these recent developments, and provides the tools necessary to develop models of phenomena important in both accelerators and cosmology. It contains a review of the Standard Model, covering non-perturbative topics, and a discussion of grand unified theories and magnetic monopoles. The book focuses on three principal areas: supersymmetry, string the- ory, and astrophysics and cosmology. The chapters on supersymmetry introduce the basics of supersymmetry and its phenomenology, and cover dynamics, dynamical supersymmetry breaking, and electric–magnetic duality. The book then introduces general relativity and the big bang theory, and the basic issues in inflationary cos- mologies. The section on string theory discusses the spectra of known string theo- ries, and the features of their interactions. The compactification of string theories is treated extensively. The book also includes brief introductions to technicolor, large extra dimensions, and the Randall–Sundrum theory of warped spaces. Supersymmetry and String Theory will enable readers to develop models for new physics, and to consider their implications for accelerator experiments. This will be of great interest to graduates and researchers in the fields of parti- cle theory, string theory, astrophysics, and cosmology. The book contains sev- eral problems and password-protected solutions will be available to lecturers at www.cambridge.org/9780521858410. Michael Dine is Professor of Physics at the University of California, Santa Cruz. He is an A. P. Sloan Foundation Fellow, a Fellow of the American Physical Society, and a Guggenheim Fellow. Prior to this Professor Dine was a research associate at the Stanford Linear Accelerator Center, a long-term member of the institute for Advanced Study, and Henry Semat Professor at the City College of the City University of New York. “An excellent and timely introduction to a wide range of topics con- cerning physics beyond the standard model, by one of the most dynamic researchers in the field. Dine has a gift for explaining difficult concepts in a transparent way. The book has wonderful insights to offer beginning graduate students and experienced researchers alike.” Nima Arkani-Hamed, Harvard University “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, its supersymmetric and grand unified extensions, and other serious models of new physics, as well as the most important experimental constraints and the realization of the key models within string theory? Dine’s book will solve most of these problems for you and give you much more, namely the state-of-the-art picture of reality as seen by a leading superstring phenomenologist.” Lubos Motl, Harvard University “This book gives a broad overview of most of the current issues in theo- retical high energy physics. It introduces and discusses a wide range of topics from a pragmatic point of view. Although some of these topics are addressed in other books, this one gives a uniform and self-contained ex- position 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 ex- pect that with the advent of the LHC a revival of model building will take place. This book is the best tool kit a modern model builder will need.” Nathan Seiberg, Institute for Advanced Study, Princeton SUPERSYMMETRY AND STRING THEORY Beyond the Standard Model MICHAEL DINE University of California, Santa Cruz cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitle:www.cambridge.org/9780521858410 © M. Dine 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2006 isbn-13 978-0-511-26009-4 eBook (EBL) isbn-10 0-511-26009-1 eBook (EBL) isbn-13 978-0-521-85841-0 hardback isbn-10 0-521-85841-0 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. This book is dedicated to Mark and Esther Dine Contents Preface page xv A note on choice of metric xviii Text website xx Part 1 Effective field theory: the Standard Model, supersymmetry, unification 1 1 Before the Standard Model3 Suggested reading7 2 The Standard Model9 2.1 Yang–Mills theory9 2.2 Realizations of symmetry in quantum field theory 12 2.3 The quantization of Yang–Mills theories 18 2.4 The particles and fields of the Standard Model 22 2.5 The gauge boson masses 25 2.6 Quark and lepton masses 27 Suggested reading 28 Exercises 28 3 Phenomenology of the Standard Model 29 3.1 The weak interactions 29 3.2 The quark and lepton mass matrices 32 3.3 The strong interactions 34 3.4 The renormalization group 35 3.5 Calculating the beta function 39 3.6 The strong interactions and dimensional transmutation 43 3.7 Confinement and lattice gauge theory 44 3.8 Strong interaction processes at high momentum transfer 51 Suggested reading 59 Exercises 61 vii viii Contents 4 The Standard Model as an effective field theory 63 4.1 Lepton and baryon number violation 66 4.2 Challenges for the Standard Model 70 4.3 The hierarchy problem 71 4.4 Dark matter and dark energy 72 4.5 Summary: successes and limitations of the Standard Model 73 Suggested reading 73 5 Anomalies, instantons and the strong CP problem 75 5.1 The chiral anomaly 76 5.2 A two-dimensional detour 81 5.3 Real QCD 89 5.4 The strong CP problem 100 5.5 Possible solutions of the strong CP problem 102 Suggested reading 105 Exercises 106 6 Grand unification 107 6.1 Cancellation of anomalies 110 6.2 Renormalization of couplings 110 6.3 Breaking to SU(3) × SU(2) × U(1) 111 6.4 SU(2) × U(1) breaking 112 6.5 Charge quantization and magnetic monopoles 113 6.6 Proton decay 114 6.7 Other groups 114 Suggested reading 117 Exercises 117 7 Magnetic monopoles and solitons 119 7.1 Solitons in 1 + 1 dimensions 120 7.2 Solitons in 2 + 1 dimensions: strings or vortices 122 7.3 Magnetic monopoles 122 7.4 The BPS limit 124 7.5 Collective coordinates for the monopole solution 125 7.6 The Witten effect: the electric charge in the presence of θ 127 7.7 Electric–magnetic duality 128 Suggested reading 129 Exercises 129 8 Technicolor: a first attempt to explain hierarchies 131 8.1 QCD in a world without Higgs fields 132 8.2 Fermion masses: extended technicolor 133 Contents ix 8.3 Precision electroweak measurements 135 Suggested reading 136 Exercises 136 Part 2 Supersymmetry 137 9 Supersymmetry 139 9.1 The supersymmetry algebra and its representations 140 9.2 Superspace 140 9.3 N = 1 Lagrangians 144 9.4 The supersymmetry currents 147 9.5 The ground-state energy in globally supersymmetric theories 148 9.6 Some simple models 149 9.7 Non-renormalization theorems 151 9.8 Local supersymmetry: supergravity 154 Suggested reading 155 Exercises 155 10 A first look at supersymmetry breaking 157 10.1 Spontaneous supersymmetry breaking 157 10.2 The goldstino theorem 160 10.3 Loop corrections and the vacuum degeneracy 161 10.4 Explicit, soft supersymmetry breaking 162 10.5 Supersymmetry breaking in supergravity models 163 Suggested reading 166 Exercises 166 11 The Minimal Supersymmetric Standard Model 167 11.1 Soft supersymmetry breaking in the MSSM 169 11.2 SU(2) × U(1) breaking 173 11.3 Why is one Higgs mass negative? 175 11.4 Radiative corrections to the Higgs mass limit 176 11.5 Embedding the MSSM in supergravity 177 11.6 The µ term 178 11.7 Constraints on soft breakings 179 Suggested reading 183 Exercises 183 12 Supersymmetric grand unification 185 12.1 A supersymmetric grand unified model 185 12.2 Coupling constant unification 186 12.3 Dimension-five operators and proton decay 188 Suggested reading 189 Exercises 189 x Contents 13 Supersymmetric dynamics 191 13.1 Criteria for supersymmetry breaking: the Witten index 192 13.2 Gaugino condensation in pure gauge theories 193 13.3 Supersymmetric QCD 194 13.4 Nf < N: a non-perturbative superpotential 197 13.5 The superpotential in the case Nf < N − 1 200 13.6 Nf = N − 1: the instanton-generated superpotential 201 Suggested reading 208 Exercises 208 14 Dynamical supersymmetry breaking 209 14.1 Models of dynamical supersymmetry breaking 209 14.2 Particle physics and dynamical supersymmetry breaking 211 Suggested reading 218 Exercises 218 15 Theories with more than four conserved supercharges