Lecture Notes in Physics

Home , Leonard Susskind, Savas Dimopoulos

Volume 939

Founding Editors W. Beiglböck J. Ehlers K. Hepp H. Weidenmüller

Editorial Board M. Bartelmann, Heidelberg, Germany P. Hänggi, Augsburg, Germany M. Hjorth-Jensen, Oslo, Norway R.A.L. Jones, Shefﬁeld, UK M. Lewenstein, Barcelona, Spain H. von Löhneysen, Karlsruhe, Germany A. Rubio, Hamburg, Germany M. Salmhofer, Heidelberg, Germany W. Schleich, Ulm, Germany S. Theisen, Potsdam, Germany D. Vollhardt, Augsburg, Germany J.D. Wells, Ann Arbor, USA G.P. Zank, Huntsville, USA The Lecture Notes in Physics

The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching-quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-deﬁned topic • to serve as an accessible introduction to the ﬁeld to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive being available at springerlink.com. The series content is indexed, abstracted and referenced by many abstracting and information services, bibliographic networks, subscription agencies, library networks, and consortia. Proposals should be sent to a member of the Editorial Board, or directly to the managing editor at Springer:

Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg/Germany [email protected]

More information about this series at http://www.springer.com/series/5304 Stuart Raby

Supersymmetric Grand Uniﬁed Theories From Quarks to Strings via SUSY GUTs

123 Stuart Raby Department of Physics The Ohio State University Columbus, Ohio, USA

ISSN 0075-8450 ISSN 1616-6361 (electronic) Lecture Notes in Physics ISBN 978-3-319-55253-8 ISBN 978-3-319-55255-2 (eBook) DOI 10.1007/978-3-319-55255-2

Library of Congress Control Number: 2017939933

© Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Printed on acid-free paper

This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland I solve physics problems while I sleep, but when awake my family always comes ﬁrst. This book is dedicated to my wife, Michele, and my children, Eric and Liat, and their families. Preface

Particle physics is the study of the fundamental building blocks of nature, i.e. the particles and their interactions. We have learned much about the four known forces of nature—the strong, weak, electromagnetic and gravitational forces. This began with the work of Coulomb, Ampére and Faraday on the phenomena of electricity and magnetism, which led to the work of Maxwell in 1863 on the unified theory of electromagnetism. The discovery of the radioactive decay of the elements in 1895 led along a jagged path to an understanding of the weak and strong forces, culminating with Einstein’s general theory of relativity in 1915. Along the way a quantum theory of nature was developed to understand the world of atoms and molecules, while Einstein’s special theory of relativity was needed to unite Newtonian mechanics with electrodynamics. Finally, these two paradigms were combined in the very successful formalism of relativistic quantum field theory. Beginning in 1905 with the discovery of the electron by J.J. Thomson, the particle zoo has grown dramatically. It now includes three families of quarks and leptons. The lightest up and down quarks are the constituents of protons and neutrons, while the lightest leptons include the electron and three types of neutrinos. The two additional families of quarks and charged leptons exist for no apparent reason. These particles and their forces are the ingredients of the Standard Model of particle physics which became complete with the discovery of the Higgs boson in 2012. The Standard Model incorporates the great success of quantum electrodynamics, using the paradigm of relativistic quantum field theory to describe all particles and their interactions via the strong, weak and electromagnetic forces. The Standard Model (plus Einstein’s gravity) describes, with amazing accuracy, phenomena on the smallest distance scales measured in the laboratory and the largest distance scales relevant for stars, planets and galaxies. It is used to understand the universe from the time of the Big Bang until the present. Whereas the Standard Model is now complete, it is far from a satisfactory theory of everything. We don’t understand why the four forces have dramatically different strengths. We don’t know why there are three families of quarks and leptons or why they have their respective masses. There is apparently an unknown dark matter and dark energy pervading the universe, and these don’t fit into the Standard Model.

vii viii Preface

We don’t understand why the three types of neutrinos are massive, but all so light. Finally, we don’t know if the four forces of nature are all that there is or whether they are completely independent. For example, we learned in 1973 that the electromagnetic and weak forces are not independent at all, but are unified into the electroweak interactions. Perhaps all the fundamental building blocks of nature, i.e. the particles and the four forces, are unified in some way. This idea receives traction from the fact that quarks and leptons are all apparently point like fundamental particles. J. Pati and A. Salam suggested in 1973 that perhaps quarks and leptons can also be unified in some big picture. It is this big picture which is the focus of this book. By 1976, when I received my Ph.D., it seemed that all the necessary theoretical ingredients of the Standard Model were present. It just took another 36 years of experiment to convincingly demonstrate this point. Upon receiving my Ph.D., I began considering physics beyond the Standard Model. Grand unification of the particles and forces had already been discussed by Howard Georgi and Sheldon Glashow in 1974. From their analysis and the work of H. Georgi, H. Quinn and S. Weinberg, it was clear that grand unified theories can unify quarks and leptons and also the strong, weak and electromagnetic forces. Proton decay was predicted to occur and experiments looking for proton decay were constructed. In 1980, while at Stanford, Leonard Susskind, Savas Dimopoulos, Hans Peter Nilles and I began studying the remarkable new theoretical construct known as “supersymmetry”. Savas and I constructed supersymmetric models of particle physics which attempted to explain why the weak scale is so much smaller than the Planck scale (where gravity becomes strong). Then in 1981, for a short period of time, Frank Wilczek, Savas and I overlapped at U.C. Santa Barbara. In this brief moment, we showed that supersymmetric grand unification was consistent with all known data. We predicted that the early experiments searching for proton decay might not see anything. Finally, just ten years later, in 1991 it was shown by the LEP experiments at CERN that supersymmetric grand unification was consistent with the measured strengths of the strong, weak and electromagnetic forces. However, gravity was still an outlier. In subsequent years many attempts have been made to combine all the known particles and forces into one unified theory. In my mind, this requires embedding any theory of particle physics into string theory, which successfully incorporates a quantum theory of gravity. In these lectures, I will describe my own attempts in this direction. To be clear, this work is not done. Moreover, at the time of this writing, it is still not known experimentally whether supersymmetry is a property of nature. Nevertheless, the theory of supersymmetric grand unification is so compelling that many physicists, including me, feel that it will eventually be discovered. Let me now begin the discussion of supersymmetric grand unified theories starting with the Standard Model and ending with a string theory description of the fundamental building blocks of nature.

Columbus, OH, USA Stuart Raby Acknowledgements

I want to thank all my collaborators and colleagues for the many discussions over the years. I have gained insight and understanding from all of you. I especially want to thank my dear friends, Leonard Susskind, Savas Dimopoulos, Hans Peter Nilles, Lawrence Hall, Graham Ross, Stefan Pokorski, Jihn E. Kim and Michael Ratz, for the many illuminating discussions. Finally, I received partial support from the Department of Energy grant, DE-SC0011726.

ix Contents

1 Introduction ...... 1 2 Brief Review of the Standard Model ...... 3 2.1 Notation ...... 3 2.2 TheStandardModel ...... 4 2.3 FermionMassesandMixing ...... 7 3 Minimal Supersymmetric Standard Model...... 11 3.1 Notation ...... 11 3.2 TheMSSM...... 12 3.3 MSSM in Terms of Component Fields ...... 14 3.4 MSSMSpectrumandSupersymmetricInteractions ...... 16 4 Soft SUSY Breaking Mechanisms ...... 19 4.1 SUSYNon-renormalizationTheorems ...... 20 4.2 SoftSUSYBreakingLagrangian ...... 23 5 Introduction to SU.5/ and SO.10/ GUTs ...... 25 5.1 TwoRoadstoGrandUnification...... 25 5.2 Introduction to SU.5/ ...... 27 5.3 Spontaneous Breaking of SU.5/ totheSM...... 30 5.4 Gauge Coupling Unification Without SUSY ...... 31 5.5 Fermion Mass Relations in SU.5/ ...... 33 5.6 Nucleon Decay ...... 34 5.7 Introduction to SO.10/ ...... 38 6 SUSY GUTs ...... 43 6.1 GUTSymmetryBreaking ...... 44 6.2 GaugeCouplingUnification ...... 45 6.3 Nucleon Decay ...... 48 6.4 Gauge Coupling Unification and Proton Decay ...... 51

xi xii Contents

7SUSYFlavorProblem...... 53 7.1 SUSYBreakingMechanisms ...... 57 8 SUSY GUTs and the CP and Flavor Problem ...... 63 8.1 RadiativeCorrectionsDuetoPhysicsAbovetheGUTScale .... 64 8.2 RadiativeCorrectionsDuetoRight-HandedNeutrinos...... 66 8.3 Summary...... 68 9 Fermion Masses and Mixing in SUSY GUTs: Predictive Theories ... 71 9.1 Complete SU.5/ SUSY GUT: GUT Breaking and Doublet-Triplet Splitting ...... 72 9.2 Complete SO.10/ Model: GUT Breaking and Doublet-Triplet Splitting ...... 77 9.3 SummaryofCompleteSUSYGUTModels...... 84 10 SO.10/ SUSY GUT and Low Energy Data ...... 87 10.1 YukawaCouplingUniﬁcation...... 87 10.2 ThirdFamilyModel ...... 88 10.3 SO.10/ GUT with D3 ŒU.1/ Z2 Z3 FamilySymmetry .... 98 10.4 The Group D3 andItsRepresentations ...... 120 11 Baryogenesis, Cosmological Moduli and Gravitino Problems, and Dark Matter...... 125 11.1 Baryogenesis via Leptogenesis...... 134 11.2 Bounds on Masses of Gravitationally Coupled Particles...... 135 11.3 DarkMatter ...... 149 12 The Little Hierarchy Problem or Fine-Tuning ...... 151 13 Problems of 4D GUTs ...... 155 14 Orbifold GUTs ...... 157 14.1 GUTsona Circle ...... 157 1 14.2 SO(3) Gauge Theory on M4 ˝ S =Z2 ...... 162 14.3 GUTsonanOrbi-Circle:BriefReview...... 167 1 0 14.4 SO.10/ in 5D on M4 ˝ S =.Z2 Z2/ ...... 168 14.5 Higgs Doublet-Triplet Splitting in Orbifold GUTs...... 170 14.6 Fermionsin5D...... 170 14.7 SupersymmetricOrbifolds...... 174 14.8 A Supersymmetric SU.5/ OrbifoldGUT...... 177 14.9 GaugeCouplingUniﬁcation...... 178 14.10 QuarksandLeptonsin5DOrbifoldGUTs...... 180 14.11 Proton Decay ...... 181 15 SO.10/ SUSY GUT in 5D ...... 185 15.1 YukawaMatrices...... 187

16 An E6 Orbifold GUT in 5D ...... 195 17 SUSY Breaking in 5D ...... 199 Contents xiii

18 SUSY GUTs in 6D: Precise Gauge Coupling Unification ...... 209 18.1 GUTBreaking ...... 211 18.2 SU.6/ ! SU.5/ U.1/X ...... 212 18.3 SU.5/ ! SU.3/ SU.2/ U.1/Y ...... 215 18.4 Proton Decay ...... 219 18.5 ThresholdCorrections...... 219 18.6 Statesatm = 0 andn = 0 ...... 221 18.7 m Axis,n = 0...... 222 18.8 n Axis,m = 0...... 223 18.9 OfftheAxes...... 223 18.10 Putting it All Together ...... 224 18.11 ResultsandDiscussion ...... 225 18.12 Summary...... 227 19 Discrete R Symmetries for the MSSM and Its Singlet Extensions .... 239 19.1 DiscreteSymmetriesoftheMSSM...... 240 ZR 19.2 A Simple 4 SymmetryintheMSSM...... 246 19.3 SingletExtensions ...... 251 19.4 Conclusions ...... 256 20 Embedding Orbifold GUTs in the Heterotic String ...... 267 20.1 EmbeddingOrbifoldGUTsintheHeteroticString...... 291 20.2 Heterotic String on a Z6 Orbifold ...... 293 20.3 HeteroticStringConstructionofEffectiveOrbifoldGUTs ...... 296 20.4 PS Model from the Z6 OrbifoldCompactification...... 297 20.5 DetailsoftheThree-FamilyPati-SalamModel ...... 305 6 21 MSSM from the Heterotic String Compactified on T =Z6 ...... 309 21.1 MSSMwithR Parity...... 310 21.2 D4 FamilySymmetry...... 312 21.3 MoreDetailsof“Benchmark”Model1...... 313 21.4 Summary...... 314 22 Gauge Coupling Unification and Proton Decay ...... 317 ZR 23 String Theory Realization of 4 Symmetry ...... 319 23.1 AnExplicitString-DerivedModel...... 323 23.2 Summary...... 330 23.3 DetailsoftheModel...... 332 24 SUSY Breaking and Moduli Stabilization ...... 337 24.1 GeneralStructure ...... 338 24.2 Moduli Stabilization and Supersymmetry Breaking intheBulk...... 348 24.3 SUSYSpectrum...... 355 24.4 Conclusions ...... 361 24.5 The Role of Holomorphic Monomials ...... 363 xiv Contents

25 Other String Constructions...... 365 25.1 SmoothHeteroticStringConstructions...... 365 25.2 TypeIIStringConstructions ...... 365 25.3 F-Theory...... 366 25.4 M-Theory...... 366 26 Epilogue ...... 369 27 Problems ...... 371 27.1 Problem1 ...... 371 27.2 Problem2 ...... 371 27.3 Problem3 ...... 372 27.4 Problem4 ...... 373 27.5 Problem5 ...... 373 27.6 Problem6 ...... 374 27.7 Problem7 ...... 374 27.8 Problem8 ...... 375 27.9 Problem9 ...... 376 27.10 Problem10...... 377 27.11 Problem11...... 377 27.12 Problem12...... 377 27.13 Problem13...... 377 28 Solutions to Problems ...... 379 28.1 SolutiontoProblem1...... 379 28.2 SolutiontoProblem2...... 379 28.3 SolutiontoProblem3...... 382 28.4 SolutiontoProblem4...... 386 28.5 SU.5/ Representations...... 386 28.6 Higgsing SU.5/ ...... 387 28.7 SolutiontoProblem5...... 390 28.8 SolutiontoProblem6...... 393 28.9 SolutiontoProblem7...... 394 28.10 SolutiontoProblem8...... 394 28.11 SolutiontoProblem9...... 397 28.12 SolutiontoProblem10 ...... 400 28.13 SolutiontoProblem11 ...... 401 28.14 SolutiontoProblem12 ...... 402 28.15 SolutiontoProblem13 ...... 405

References...... 409