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

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.

arXiv comment17 pages. v4: some coefficients of quadratic divergences in appendix B corrected

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• On gauge dependence of the one-loop divergences in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ SYM theories
• Higher Derivative Gauge theory in $d=6$ and the $\mathbb{C}{\mathbb{P}}^{(N_f-1)}$ NLSM
• Six dimensional ultraviolet completion of the $CP(N)$ $\sigma$ model at two loops
• One-loop divergences in the six-dimensional $\mathcal{N}=(1,0)$ hypermultiplet self-coupling model
• Supersymmetry at BLTP: Recent Progress in Two Directions