Abstract
We analyze the constraints imposed by gauge invariance on higher-order interactions between massless bosonic fields in three-dimensional higher-spin gravities. Focusing on the transverse-traceless part, we show that vertices of quartic and higher order that are independent of the cubic ones can only involve scalars and Maxwell fields. As a consequence, the full nonlinear interactions of massless higher-spin fields are completely fixed by the cubic vertex.
Highlights
University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria and Erwin Schrödinger International Institute for Mathematics and Physics, Boltzmanngasse 9, 1090 Vienna, Austria
Introduction.—In this Letter, we start an investigation aimed at a Lagrangian formulation of three-dimensional (3D) higher-spin (HS) gravities [1] beyond cubic order
No nonlinear Lagrangian of interacting Fronsdal fields is known, but there is a systematic perturbative approach to construct such Langrangians. This is known as the Noether-Fronsdal program, which we follow in this work and review below
Summary
It is described by the quadratic Fronsdal Lagrangian L2 [2]. There are different motivations to study HS gravities (d þ 1)-dimensional HS gravity theory on asymptotically AdS space-times is related to a d-dimensional conformal field theory (CFT) This HS AdS=CFT correspondence [3,4] is a priori independent of the string-theoretic AdS=CFT correspondence, and possesses distinct features as it does not require supersymmetry and is accessible to perturbative checks. In the Noether procedure one starts with the free quadratic Lagrangian L2 and builds vertices order by order, 0031-9007=19=123(13)=131601(5)
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