# Super Heat Kernel and One-Loop Divergence of Super Yang-Mills Theory in Conformal Supergravity

## TL;DR

This paper develops a super heat kernel method to compute one-loop divergences in super Yang-Mills theory within conformal supergravity, providing a systematic approach to quantum corrections in supersymmetric gauge theories.

## Contribution

It introduces a non-iterative scheme for calculating super heat kernel coefficients, including the first three that determine one-loop divergences, applicable to various quantum theories.

## Key findings

- Derived the full one-loop divergence of SYM in conformal supergravity.
- Calculated the first three super heat kernel coefficients.
- Presented a general method for higher order coefficient derivation.

## Abstract

We consider super Yang-Mills Theory in $N=1$ conformal supergravity. Using the background field method and the Feddeev-Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.