Extended vector-tensor theories

TL;DR

This paper develops a comprehensive class of massive vector-tensor theories in curved space-time, ensuring the correct number of degrees of freedom and exploring their properties under various transformations.

Contribution

It introduces a new class of degenerate vector-tensor theories with up to two derivatives, unifying and extending previous generalized Proca models in curved space.

Findings

Theories propagate five degrees of freedom, including three massive vector and two tensor modes.

Generalized Proca and beyond generalized Proca theories are shown to be degenerate in curved space.

Theories exhibit specific transformation properties under metric and vector field changes.

Abstract

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.