Geometric Formulation for Partially Massless Fields

TL;DR

The paper develops a geometric, frame-like formulation for free symmetric partially massless fields in $(A)dS_d$ by describing PM fields as 1-form connections valued in $o(d-1,2)\oplus o(d,1)$ with two-row Young tableau symmetry. It constructs gauge-invariant linearized curvatures and covariant actions $S^{s,t}$, detailing both $(A)dS_d$ and Lorentz-covariant presentations, and demonstrates the approach with explicit spin-2 and spin-3 PM examples. The results clarify the PM gauge structure, identify generalized Weyl tensors as physical invariants, and show how flat limits reproduce sums of massless actions, while imposing constraints that may narrow allowed higher-spin algebras to those compatible with unitarity. The work suggests extensions to mixed-symmetry PM fields and discusses implications for the organization and consistency of HS gauge theories.

Abstract

The manifestly gauge invariant formulation for free symmetric partially massless fields in $(A)dS_d$ is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of $(o(d-1,2)) o(d,1)$ described by two-row Young tableaux, in which the lengths of the first and second row are, respectively, associated with spin and depth of partial masslessness.