On Interacting Higher Spin Bosonic Gauge Fields in BRST-antifield Formalism

TL;DR

This paper develops a method to construct interacting higher spin bosonic gauge field actions within the BRST-antifield formalism, successfully extending free theories to all orders in the interaction parameter and applying to anti-de Sitter spaces.

Contribution

It presents a systematic approach to solving the master equation for interacting higher spin gauge fields, including their extension to anti-de Sitter backgrounds.

Findings

Successfully constructed all-order interacting actions from cubic deformations.

Extended free higher spin theories to anti-de Sitter spaces.

Maintained anti-ghost number constraint in the constructed actions.

Abstract

We examine interacting bosonic higher spin gauge fields in the BRST-antifield formalism. Assuming that an interacting action $S$ is a deformation of the free action with a deformation parameter $g$, we solve the master equation $(S,S)=0$ from the lower orders in $g$. It is shown that choosing a certain cubic interaction as the first order deformation, we can solve the master equation and obtain an action containing all orders in $g$. The anti-ghost number of the obtained action is less than or equal to two. Furthermore we show that the obtained action is lifted to that of interacting bosonic higher spin gauge fields on anti-de Sitter spaces.