Cubic interactions of Maxwell-like higher spins

Abstract

We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure allowing to systematically account for the deformations of the transversality conditions to be imposed on the gauge parameters at the free level.

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…[47][48][49][50], while, in the framework of ambient space metric-like approach, interacting higher-spin AdS fields are considered in refs. [51][52][53][54][55][56]. 11 In this respect, recent interesting discussion of 11 In frame-like approach, equations of motion for continuous-spin field were studied in ref.…”

4D higher spin black holes with nonlinear scalar fluctuations

“…One of the outstanding problems is to connect two different approaches to higher spin gravity that are presently pursued: Vasiliev's theory and the quasi-local deformed Fronsdal theory. The latter approach (see [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] and references therein; see also [59] for a review and more references, and [109][110][111][112][113] for more recent works on the holographic reconstruction of bulk vertices) provides a perturbatively defined deformation of the free Fronsdal action following the Noether procedure supplemented by weak locality conditions -as to ensure well-defined amplitudes built using Green's functions in anti-de Sitter spacetime with proper boundary conditions. Up to quartic order, this approach has so far been yielding holographic correlation functions corresponding to unitary free conformal field theories.…”

Unfree gauge symmetry in the Hamiltonian formalism

“…The role of the modular parameter is played by the cosmological constant, while the completion function is the scalar curvature. Unfree gauge symmetries of some higher spin field theories, see [12], [13], [14], [15], also follow the pattern of this example, though the completion functions are tensors in these models, not scalars.…”

“…The field theories with unfree gauge symmetry represent a special class of models where the gauge parameters have to obey differential equations. Every known example of these theories (see [3]- [15] and references therein) admits an "almost equivalent" analogue without constraints on gauge parameters. The subtle difference is that the models with unfree gauge symmetry comprise dynamics with arbitrary modular parameters, which are involved as integration constants, while the analogues explicitly involve fixed modular parameters.…”

“…For discussion of consequences of transversality condition in the unimodular gravity and various extensions, see [3], [4], [5], [6], [7], [8], [9], [10], [11] and references therein. More examples of unfree gauge symmetry can be found among multifarious higher spin field theories, see [12], [13], [14], [15].…”