One-loop effective actions and higher spins. II

TL;DR

This paper extends the analysis of effective actions from scalar and fermion fields coupled to external sources, focusing on geometrization, off-shell covariance, and comprehensive two-point correlator results for spins up to 5 across multiple dimensions.

Contribution

It introduces a covariant geometrization of effective actions and provides an extensive set of two-point correlator results for higher spins in various dimensions.

Findings

Expressed effective actions in terms of covariant Jacobi tensors.

Addressed tadpoles and seagull terms for off-shell covariance.

Compiled all two-point correlators for spins up to 5 in dimensions 3 to 6.

Abstract

In this paper we continue and improve the analysis of the effective actions obtained by integrating out a scalar and a fermion field coupled to external symmetric sources, started in the previous paper. The first subject we study is the geometrization of the results obtained there, that is we express them in terms of covariant Jacobi tensors. The second subject concerns the treatment of tadpoles and seagull terms in order to implement off-shell covariance in the initial model. The last and by far largest part of the paper is a repository of results concerning all two point correlators (including mixed ones) of symmetric currents of any spin up to 5 and in any dimensions between 3 and 6. In the massless case we also provide formulas for any spin in any dimension.