Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields

TL;DR

Massive higher-spin fields pose consistency challenges beyond the massless limit. The paper develops a frame-like unfolded formulation for symmetric massive HS fields in Minkowski and $(A)dS$, yielding a manifestly gauge-invariant action built from curvatures and a closed system of unfolded equations. The approach uses 1-form connections and 0-form Weyl tensors valued in Lorentz representations described by two-row Young tableaux, with curvature $R^{\alpha}=dW^{\alpha}+G^{\alpha}(W)$ and compatibility $G^{\beta} (\delta^L G^{\alpha}/\delta W^{\beta})=0$, and it demonstrates that 0-forms are necessary for massive fields. The results provide explicit unfolded equations for spin $s$ massive symmetric fields and a gauge-invariant action, offering a framework for HS symmetry breaking and potential links to String Theory.

Abstract

Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS spaces are presented. Manifestly gauge invariant action for a spin $s \ge 2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.