Tensor gauge fields in arbitrary representations of GL(D,R): II. Quadratic actions

TL;DR

This paper constructs explicit quadratic actions for tensor gauge fields in arbitrary representations of GL(D,R), ensuring correct physical degrees of freedom and providing a frame-like reformulation without trace constraints.

Contribution

It introduces a compact, explicit form of quadratic actions for tensor gauge fields in arbitrary representations, extending previous non-Lagrangian equations to a Lagrangian framework.

Findings

Actions propagate correct massless degrees of freedom

Equivalence to previously proposed local equations

Frame-like reformulation without trace constraints

Abstract

Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of Levi-Civita tensors. The field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non-Lagrangian local field equations proposed previously. Moreover, these actions allow a frame-like reformulation a la MacDowell-Mansouri, without any trace constraint in the tangent indices.