Effective action for higher spin fields on (A)dS backgrounds

TL;DR

This paper develops a method to compute the one-loop effective action for higher spin fields on (A)dS backgrounds using a first-quantized approach with spinning particles, simplifying gauge fixing and extracting heat kernel coefficients.

Contribution

It introduces a first-quantized description for higher spin fields on (A)dS spaces, enabling explicit calculation of the effective action and heat kernel coefficients.

Findings

Derived a representation of the one-loop effective action on (A)dS.

Computed the first few heat kernel coefficients for arbitrary even dimensions.

Simplified gauge fixing procedure on conformally flat backgrounds.

Abstract

We study the one loop effective action for a class of higher spin fields by using a first-quantized description. The latter is obtained by considering spinning particles, characterized by an extended local supersymmetry on the worldline, that can propagate consistently on conformally flat spaces. The gauge fixing procedure for calculating the worldline path integral on a loop is delicate, as the gauge algebra contains nontrivial structure functions. Restricting the analysis on (A)dS backgrounds simplifies the gauge fixing procedure, and allows us to produce a useful representation of the one loop effective action. In particular, we extract the first few heat kernel coefficients for arbitrary even spacetime dimension D and for spin S identified by a curvature tensor with the symmetries of a rectangular Young tableau of D/2 rows and [S] columns.