On gauge dependence of the one-loop divergences in 6D, N=(1,0) and N=(1,1) SYM theories

Abstract

We study the gauge dependence of one-loop divergences in a general matter-coupled 6D, N=(1,0) supersymmetric gauge theory in the harmonic superspace formulation. Our analysis is based on the effective action constructed by the background superfield method, with the gauge-fixing term involving one real parameter ξ0. A manifestly gauge invariant and N=(1,0) supersymmetric procedure for calculating the one-loop effective action is developed. It yields the one-loop divergences in an explicit form and allows one to investigate their gauge dependence. As compared to the minimal gauge, ξ0=1, the divergent part of the general-gauge effective action contains a new term depending on ξ0. This term vanishes for the background superfields satisfying the classical equations of motion, so that the S-matrix divergences are gauge-independent. In the case of 6D, N=(1,1) SYM theory we demonstrate that some divergent contributions in the non-minimal gauges do not vanish off shell, as opposed to the minimal gauge.