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

Abstract

We study the gauge dependence of one-loop divergences in a general matter-coupled $6D$, $\mathcal{N}=(1,0)$ 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 ${\xi }_0$. A manifestly gauge invariant and $\mathcal{N}=(1,0)$ 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, ${\xi }_0=1$, the divergent part of the general-gauge effective action contains a new term depending on ${\xi }_0$. 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 $6D$, $\mathcal{N}=(1,1)$ SYM theory we demonstrate that some divergent contributions in the non-minimal gauges do not vanish off shell, as opposed to the minimal gauge.

13 pages

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Cited by in corpus (5)

• The renormalization structure of $6D$, $\mathcal{N}=(1,0)$ supersymmetric higher-derivative gauge theory
• On the component structure of one-loop effective actions in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetric gauge theories
• On the two-loop divergences in 6D, $\mathcal{N}=(1,1)$ SYM theory
• Low-energy $6D$, $\mathcal{N}=(1,1)$ SYM effective action beyond the leading approximation
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions