On Killing tensors and cubic vertices in higher‐spin gauge theories

Abstract

Based on a talk given by X.B. at the RTN Workshop "Constituents, Fundamental Forces and Symmetries of the Universe" (Corfu, 20-26th September 2005). Contribution to the Proceedings. AbstractThe problem of determining all consistent non-Abelian local interactions is reviewed in flat space-time. The antifield-BRST formulation of the free theory is an efficient tool to address this problem. Firstly, it allows to compute all on-shell local Killing tensor fields, which are important because of their deep relationship with higher-spin algebras. Secondly, under the sole assumptions of locality and Poincaré invariance, all non-trivial consistent deformations of a sum of spin-three quadratic actions deforming the Abelian gauge algebra were determined. They are compared with lower-spin cases.

Universal limits on massless high-spin particles

“…No example of consistent interactions of this type exists for spin s > 2. Indeed, theorems proving the opposite in fairly general cases have been already given in the literature [24,25,26].…”

Notes on higher-spin algebras: minimal representations and structure constants

“…The space of the solutionsε µ 1 ···µr -Killing tensors -defines the HS algebra as a vector space (see [60,61] for related works). For more details, it is convenient to reiterate the discussion using auxiliary variables in the ambient-space formulation.…”

Actions, Charges and Off-Shell Fields in the Unfolded Dynamics Approach

“…The formulation of the HS dynamics in AdS d developed in [2] gives both the off-shell formulation (as was emphasized in [5]) and on-shell formulation. The latter results from factorization of the ideal associated with the off-shell degrees of freedom that are trivial on-mass-shell [2] (for more details see [6]). As shown originally in [7], consistent HS interactions with gravity require AdS background with non-zero cosmological constant as the most symmetric vacuum.…”

“…So far the unfolded formulation was applied [3] (see also [8,9,6] for reviews) to the analysis of the field equations and/or constraints. In this paper we extend this approach to the action level.…”

“…Note that every universal free differential algebra is associated with some L ∞ algebra 1 [10]. The condition (2.4), which can equivalently be rewritten as 6) guarantees the formal consistency of the unfolded system (2.1) with d 2 = 0 for all W α . This form of the compatibility condition manifests close relation of our construction with Q-manifolds [14] and, more generally, with the Batalin-Vilkovisky approach [15] (see [16] for a recent discussion of the latter relationship).…”