RevModPhys.84.987

2012 84398723 2 dynamical symmetry breaking spin one

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Unformatted text preview: 3)=987(23) 2. Dynamical symmetry breaking: Spin one versus higher spin V. Fully Interacting Example: Vasiliev’s Higher-Spin Gravity A. Examples of non-Abelian gauge theories B. The need for a complete theory C. Vasiliev’s equations D. AdS/CFT correspondence: Vasiliev’s theory from free conformal fields E. Emergence of extended objects VI. Conclusions and Outlook Appendix A: Weinberg Low-energy Theorem: S matrix and Lagrangian Dictionary 1. Emission of a massless particle: Lorentz versus gauge invariances 2. Cubic vertices Appendix B: Weinberg-Witten Theorem: A Lagrangian Reformulation 1. Weinberg-Witten theorem 2. Refinement of Weinberg-Witten theorem 987 Ó 2012 American Physical Society 988 Xavier Bekaert, Nicolas Boulanger, and Per A. Sundell: How higher-spin gravity surpasses the spin- . . . interacting quantum field theory.2 While this may seem to call for radical measures, there exists a relatively conservative yet viable way out, namely, the dual usage of the cosmological constant as critical mass (infrared cutoff) and dimensionful coupling constant. This dual-purpose treatment of the cosmological constant leads to a successful exchange of what are leading and subleading terms in minimal coupling that lifts the spell of the no-go theorems, and, in particular, reconciles higher-spin gauge symmetry with the equivalence principle, leading up to the FradkinVasiliev cubic action (Fradkin and Vasiliev, 1987b, 1987c; Vasiliev, 2001a, 2011; Alkalaev and Vasiliev, 2003) and Vasiliev’s fully nonlinear equations of motion3 (Vasiliev, 1990, 1992, 2003) [see, e.g., Vasiliev (2004a, 2004b) and Bekaert and et al. (2005) for some reviews]. Since our aim is to outline main ideas and results, we refrain from being technical and refer the interested reader to the already existing literature whenever necessary. Moreover, throughout the paper we mostly stick to the Fronsdal program (Fronsdal, 1978), i.e., the standard perturbative off-shell implementation of non-Abelian gauge deformations starting from the Fronsdal actions in constantly curved backgrounds. It is the gauge algebra (not necessarily an internal algebra) that we require to become non-Abelian similar to the diffeomorphism algebra in Einstein gravity. As for Vasiliev’s higher-spin gravity, presently the most far-reaching construction of a full higher-spin gauge theory, we restrict ourselves4 to a more brief address of how it presents a natural framework for a string-theory-like double perturbative expansion. Now, why are higher-spin gauge fields interesting? Although massless fields of spin greater than 2 make perfect sense at the free level, their quantum interactions pose a main challenge to modern theoretical physics. In a nutshell, the problematics can be summarized as follows: consistent nonAbelian higher-spin gauge symmetries induce local higherderivative generalizations of translations that seem to call for a nontrivial bosonic extension of spacetime itself, thus interfering with...
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