RevModPhys.84.987

RevModPhys.84.987 - REVIEWS OF MODERN PHYSICS VOLUME 84...

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How higher-spin gravity surpasses the spin-two barrier Xavier Bekaert * Laboratoire de Mathe ´matiques et Physique The ´orique, Unite ´ Mixte de Recherche 7350 du CNRS, Fe ´de ´ration de Recherche 2964 Denis Poisson, Universite ´ Franc ¸ois Rabelais, Parc de Grandmont, 37200 Tours, France Nicolas Boulanger and Per A. Sundell Service de Me ´canique et Gravitation, Universite ´ de Mons—UMONS, 20 Place du Parc, 7000 Mons, Belgium (published 3 July 2012) Aiming at nonexperts, the key mechanisms of higher-spin extensions of ordinary gravities in four dimensions and higher are explained. An overview of various no-go theorems for low-energy scattering of massless particles in Fat spacetime is given. In doing so, a connection between the S -matrix and the Lagrangian approaches is made, exhibiting their relative advantages and weaknesses, after which potential loopholes for nontrivial massless dynamics are highlighted. Positive yes-go results for non-Abelian cubic higher-derivative vertices in constantly curved backgrounds are reviewed. ±inally, how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the ±radkin-Vasiliev vertices and Vasiliev’s higher-spin gravity with its double perturbative expansion (in terms of numbers of ²elds and derivatives) is outlined. DOI: 10.1103/RevModPhys.84.987 PACS numbers: 04.60. ± m, 11.15.Pg, 11.30.Ly, 14.80. ± j CONTENTS I. Introduction 987 II. No-go Theorems in ±lat Spacetime 990 A. Preamble: The gauge principle and the ±ronsdal program 990 B. The Weinberg low-energy theorem 990 1. Charge conservation: The spin-one case 990 2. Equivalence principle: The spin-two case 991 3. Higher-order conservation laws: The higher-spin cases 991 C. Coleman-Mandula theorem and its avatar: No higher-spin conserved charges 991 D. Generalized Weinberg-Witten theorem 992 E. Velo-Zwanziger dif²culties 992 III. Possible Ways Out 993 A. Masslessness 993 B. Asymptotic states and conserved charges 993 C. Lorentz minimal coupling 994 D. ±lat background 994 E. ±inite dimensionality of spacetime 994 IV. Various Yes-go Examples 994 A. Consistent cubic vertices in Minkowski spacetime 995 B. Cubic vertices in AdS spacetime 996 C. Main lessons 997 D. Higher-spin symmetry breakings 998 1. Higher-spin gauge symmetries are broken at the infrared scale 999 2. Dynamical symmetry breaking: Spin one versus higher spin 999 V. ±ully Interacting Example: Vasiliev’s Higher-Spin Gravity 999 A. Examples of non-Abelian gauge theories 999 B. The need for a complete theory 1000 C. Vasiliev’s equations 1001 D. AdS/C±T correspondence: Vasiliev’s theory from free conformal ²elds 1001 E. Emergence of extended objects 1003 VI. Conclusions and Outlook 1004 Appendix A: Weinberg Low-energy Theorem: S matrix and Lagrangian Dictionary 1004 1. Emission of a massless particle: Lorentz versus gauge invariances 1004 2. Cubic vertices 1005 Appendix B: Weinberg-Witten Theorem: A Lagrangian Reformulation 1005 1. Weinberg-Witten theorem 1005 2. Re²nement of Weinberg-Witten theorem 1006 I. INTRODUCTION This review is an attempt at a nontechnical summary of
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RevModPhys.84.987 - REVIEWS OF MODERN PHYSICS VOLUME 84...

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