RevModPhys.84.987

And will be reviewed here as well as their relations

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Unformatted text preview: as well as their relations with the Fradkin-Vasiliev vertices. In summary, it may prove to be useful to confront the no-go theorems with the yes-go examples already in the classical Lagrangian framework, in order to emphasize the underlying assumptions of the no-go theorems, even if it may require an extra assumption about perturbative locality. The paper is organized as follows: In Sec. II we begin by spelling out the gauge principle in perturbative quantum field theory and its ‘‘standard’’ implementation within the Fronsdal program for higher-spin gauge interactions. We then survey the problematics of nontrivial scattering of massless particles of spin greater than 2 in flat spacetime, and especially its direct conflict with the equivalence principle. In Sec. III we list possible ways to evade these negative results, both within and without the Fronsdal program. In Sec. IV we review results where consistent higher-spin interactions have been found, in both flat and (A)dS spacetimes. Because of the fact that consistent interacting higher-spin gravities indeed exist, at least for gauge algebras which are infinite-dimensional extensions of the (A)dS isometry algebra, an important question is related to the possible symmetry breaking mechanisms that give a mass to the higher-spin gauge fields. This is briefly discussed in Sec. IV.D. After reviewing why a classically complete theory is crucial in higher-spin gravity, we lay out in Sec. V the salient features of Vasiliev’s approach to a class of potentially viable models of quantum gravity. We conclude in Sec. VI where we also summarize some interesting open problems. Finally we devote two Appendixes to the review of some S-matrix no-go theorems and to their reformulation in Lagrangian language. More precisely, Appendix A focuses on Weinberg’s lowenergy theorem, while Appendix B concentrates on the Weinberg-Witten theorem and its recent adaptation to gauge theories by Porrati. II. NO-GO THEOREMS IN FLAT SPACETIME This section presents various theorems7 that constrain interactions between massless particles in flat spacetime, potentially ruling out nontrivial quantum field theories with gauge fields with spin s > 2 and vanishing cosmological constant. The aim is to scrutinize some of their hypotheses in order to exhibit a number of conceivable loopholes that may lead to modified theories including massless higher spin, as summarized in Sec. III. ance in perturbative quantum field theory stems from the fact that one and the same massless particle, thought of as a representation of the spacetime isometry group, in general admits (infinitely) many implementations in terms of quantum fields sitting in different Lorentz tensors obeying respective free equations of motion. For more information, see, e.g., Skvortsov (2008) and Boulanger, Iazeolla, and Sundell (2009). Only a subset of these ‘‘carriers,’’ namely, the primary curvature tensors and all of their derivatives, actu...
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