Equation for one-loop divergences in two dimensions and its application to higher spin fields

TL;DR

This paper derives a simple formula for one-loop divergences in two-dimensional curved space-time, enabling calculations for higher spin fields and demonstrating gauge independence and spin invariance for certain cases.

Contribution

It introduces a new, straightforward formula for one-loop divergences applicable to nonminimal second order operators in two dimensions, facilitating higher spin field analysis.

Findings

The formula simplifies divergence calculations in 2D curved space.

One-loop divergences for higher spin fields are gauge independent.

Results are independent of spin for s ≥ 3.

Abstract

A simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space-time is derived for theories for which the second variation of the action is a nonminimal second order operator with small nonminimal terms. In particular, this formula allows to calculate terms which are integrals of total derivatives. As an application of the result, one-loop divergences for the higher spin fields on the constant curvature background are obtained in a nonminimal gauge, which depends on two parameters. By an explicit calculation we demonstrate that with the considered accuracy the result is gauge independent. Moreover, the result appeared to be independent of the spin $s$ for $s\ge 3$.