# One-loop beta-functions in 4-derivative gauge theory in 6 dimensions

## TL;DR

This paper computes the one-loop beta-functions for a class of 6-dimensional 4-derivative gauge theories, including a supersymmetric case, using the background field method and deriving the necessary Seeley-DeWitt coefficient.

## Contribution

It introduces a systematic method to compute the $b_6$ Seeley-DeWitt coefficient for 4-derivative operators and applies it to determine beta-functions in 6d gauge theories.

## Key findings

- Derived the $b_6$ Seeley-DeWitt coefficient for generic 4-derivative operators.
- Calculated the one-loop beta-functions for a classically scale-invariant 6d gauge theory.
- Computed the beta-function for a supersymmetric (1,0) 6d gauge theory.

## Abstract

A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative $ (\nabla F)^2 + F^3$ gauge theory with two independent couplings. Motivated by a search for a perturbatively conformal but possibly non-unitary 6d models we compute the one-loop $\beta$-functions in this theory. A systematic way of doing this using the background field method requires the expression for the $b_6$ Seeley-DeWitt coefficient for a generic 4-derivative operator. It was previously unknown and we derive it here. As an application, we also compute the one-loop $\beta$-function in the (1,0) supersymmetric $ (\nabla F)^2$ 6d gauge theory constructed in hep-th/0505082.