Massive gauge-invariant field theories on spaces of constant curvature

TL;DR

This paper develops gauge-invariant field theories for mixed symmetry bosonic fields on constant curvature spaces, detailing actions, auxiliary fields, and mass regimes, with implications for string theory compactifications.

Contribution

It introduces a framework for constructing gauge-invariant actions for mixed symmetry fields with two-column Young tableaux on curved backgrounds, including massless limits.

Findings

Explicit gauge-invariant actions derived for fields with two-column Young tableaux.

Analysis of massless and partially massless regimes in these theories.

Comments on extending the structure to arbitrary Young tableaux.

Abstract

Gauge fields of mixed symmetry, corresponding to arbitrary representations of the local Lorentz group of the background spacetime, arise as massive modes in compactifications of superstring theories. We describe bosonic gauge field theories on constant curvature spaces whose fields are in irreducible representations of the general linear group corresponding to Young tableaux with two columns. The gauge-invariant actions for such fields are given and generally require the use of auxiliary fields and additional mass-like terms. We examine these theories in various (partially) massless regimes in which each of the mass-like parameters vanishes. We also make some comments about how the structure extends for gauge fields corresponding to arbitrary Young tableaux.