Notes on conformal invariance of gauge fields

TL;DR

This paper investigates the conformal invariance of free higher spin gauge fields, revealing that most such fields are not conformal in Minkowski and (A)dS spaces, using a novel approach based on reducibility parameters.

Contribution

The paper introduces a new method leveraging reducibility parameters to analyze conformal invariance of higher spin gauge fields, extending to non-Lagrangian systems.

Findings

Massless higher spin gauge fields in Minkowski space are not conformal for spin > 1.

Partially-massless fields in (A)dS space are not conformal for spin > 1.

Maximal-depth partially-massless fields in 4D are not conformal, unlike some related fields.

Abstract

In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.