Induced Action for Conformal Higher Spins from Worldline Path Integrals

TL;DR

This paper develops a worldline path integral approach to conformal higher spin fields, providing a new representation of their action and quadratic terms, with future plans to explore interactions.

Contribution

It introduces a worldline particle model to derive the conformal higher spin action from a one-loop scalar effective action, offering a novel computational perspective.

Findings

Derived the quadratic part of the CHS action from worldline path integrals.

Provided a worldline representation for the CHS action.

Set the stage for future computation of cubic and higher-order vertices.

Abstract

Conformal higher spin (CHS) fields, despite being non unitary, provide a remarkable example of a consistent interacting higher spin theory in flat space background, that is local to all orders. The non-linear action is defined as the logarithmically UV divergent part of a one-loop scalar effective action. In this paper we take a particle model, that describes the interaction of a scalar particle to the CHS background, and compute its path integral on the circle. We thus provide a worldline representation for the CHS action, and rederive its quadratic part. We plan to come back to the subject, to compute cubic and higher vertices, in a future work.