Higher spin interactions: cubic deformations on Minkowski and (Anti)de Sitter backgrounds

TL;DR

This thesis reviews the construction and analysis of cubic higher-spin interactions in Minkowski and (Anti)de Sitter spacetimes, establishing correspondences and examining consistency of various solutions.

Contribution

It provides a comprehensive review of first-order cubic deformations using the antifield formalism and establishes a link between (A)dS and Minkowski cubic vertices, including the uniqueness of certain deformations.

Findings

Identified consistent cubic vertices in Minkowski spacetime for various spin triplets.

Established a correspondence between (A)dS and Minkowski cubic vertices.

Showed the inconsistency of several cubic solutions at second order.

Abstract

In the thesis, results presented in various papers involving the author are reviewed. First, general results about consistent deformations at first order (i.e. cubic) using the antifield formalism in Minkowski spacetime are gathered. Secondly, a correspondance between the consistent nonabelian cubic vertices in (Anti)de Sitter and those in Minkowski spacetime is establish. The Minkowski nonabelian cubic solutions for the triplets of spin 2-2-3, 3-3-3 (in particular the parity-breaking ones), 1-s-s and 2-s-s are then studied, the last of which providing the uniqueness of the 2-s-s Fradkin-Vasiliev deformation procedure in (A)dS spacetime. Finally, we carry out second order computations in Minkowski spacetime that show the inconsistency of several cubic solutions, including the spin-3 Berends-Burgers-van Dam vertex.