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 (del 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 back-ground field method requires the (previously unknown) expression for the b(6) Seeley-DeWitt coefficient for a generic 4-derivative operator; we derive it here. As an application, we also compute the one-loop beta-function in the (1,0) supersymmetric (del F)(2) 6d gauge theory con-structed in hep-th/0505082.