Massive gauge-invariant field theories on spaces of constant curvature

TL;DR

The paper develops a finite, gauge-invariant framework for bosonic gauge fields in mixed symmetry types on spaces of constant curvature, focusing on two-column Young tableaux [p,q]. It constructs a robust bi-form (and multi-form) formalism, derives appropriate field strengths and generalized Einstein tensors, and analyzes massless, partially massless, and massive regimes, including curvature-induced mass terms and unitarity bounds in AdS/dS. Massless theories exist in flat space for p=q or q=0, while curved space typically requires auxiliary fields to achieve full invariance; massive theories employ compensators whose number grows with the number of columns, with a detailed curved-space structure linking mass parameters to the cosmological constant. The results generalize to arbitrary Young tableaux via the multi-form construction, providing a finite, gauge-invariant description of higher-spin/mixed-symmetry fields in curved backgrounds with implications for string compactifications and higher-spin theories.

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.