One-loop β-functions in 4-derivative gauge theory in 6 dimensions

A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative (∇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 β-functions in this theory. A systematic way of doing this using the back-ground field method requires the (previously unknown) expression for the b₆ Seeley-DeWitt coefficient for a generic 4-derivative operator; we derive it here. As an application, we also compute the one-loop β-function in the (1,0) supersymmetric (∇F )² 6d gauge theory con-structed in <ExternalRef> <RefSource>hep-th/0505082</RefSource> <RefTarget Address="http://arxiv.org/abs/hep-th/0505082" TargetType="URL"/> </ExternalRef>.