RevModPhys.84.987

May play in order to have a phenomenologically viable

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Unformatted text preview: y three classes of models containing local degrees of freedom:  Yang-Mills theories, i.e. the theory of self-interacting set of spin-one fields;  general relativity, i.e. the theory of a self-interacting spin-two field; and  higher-spin gravity, i.e., the theory of a self-interacting tower of critically massless even-spin fields. Looking to their classical perturbation theories, one sees that higher-spin gravity distinguishes itself in the sense that it does not admit a strictly massless perturbative formulation on shell in terms of massless fields in flat spacetime. Instead it admits a generally covariant double perturbative expansion in powers of the following22:  a dimensionless coupling constant g counting the numbers of weak fields; and  the inverse of a cosmological constant à counting the numbers of pairs of derivatives. Although higher-spin gravity still lacks a standard off-shell formulation, its on-shell properties nonetheless suggest a quantum theory in AdS spacetime in which localized higher-spin quanta interact in such a fashion that the resulting low-energy effective description be dominated by higherderivative vertices such that the standard minimal spin-two couplings show up only as a subleading term. Thus one may think of higher-spin gravity as an effective flat-space quantum field theory with an exotic cutoff: a finite infrared cutoff, showing up as a cosmological constant in the gravitational perturbation theory, that at the same time plays the role of a massive parameter in higher-derivative interactions. We mention again that the reason for this state of affairs can be explained directly in terms of the (mainly negative) results for higher-spin gauge theory in flat spacetime: if one removes Ã, i.e., attempts to formulate a strictly massless higher-spin gauge theory without any infrared cutoff, then one falls under the spell of various powerful (albeit restricted) no-go theorems concerning the couplings between massless fields with spin s > 2 and massless fields with spins s 2 in flat spacetime. As mentioned, the perhaps most striking constraint on gauge theories with vanishing cosmological constant à ¼ 0 is the clear-cut clash between the equivalence principle, which essentially concerns the non-Abelian nature of spintwo gauge symmetries, and Abelian higher-spin gauge symmetry: on the one hand, all massless (as well as massive) fields must couple to a massless spin-two field via twoderivative vertices with the same universal coupling constant; on the other hand, such minimal couplings are actually incompatible with the free gauge transformations for spin-s > 2 fields as long as one assumes that these couplings play the dominant role at low energies. pffiffiffiffiffiffiffi One can also define a Planck length ‘p ¼ g jÃj, but unlike general relativity, which contains only two derivatives, higher-spin gravity has no sensible expansion (in its unbroken phase) in powers of ‘p . In this sense, the per...
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