All spin-2 cubic vertices with two derivatives

TL;DR

This paper systematically classifies all possible three-field interaction vertices for spin-2 particles with two derivatives in (anti) de Sitter space, covering various mass configurations and their relevance to gravity theories.

Contribution

It provides a complete enumeration of spin-2 cubic vertices with two derivatives in (A)dS space, considering different mass and field configurations, without auxiliary fields.

Findings

List of all cubic vertices with two derivatives for spin-2 fields.

Analysis of vertices involving massive, massless, and partially massless fields.

Discussion of implications for (bi)gravity theories.

Abstract

In this paper we provide a complete list of spin-2 cubic interaction vertices with two derivatives. We work in (anti) de Sitter space with dimension d >= 4 and arbitrary value of cosmological constant and use simple metric formalism without any auxiliary or Stueckelberg fields. We separately consider cases with one, two and three different spin-2 fields entering the vertex where each field may be massive, massless or partially massless one. The connection of our results with massive (bi)gravity theories is also briefly discussed.