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arXiv · 1907.12302

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

I. L. Buchbinder·E. A. Ivanov·B. S. Merzlikin·K. V. Stepanyantz
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Abstract

We study the gauge dependence of one-loop divergences in a general matter-coupled $6D$, ${\cal N}=(1,0)$ 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 ${\cal N}=(1,0)$ 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 $6D$, ${\cal N} = (1,1)$ SYM theory we demonstrate that some divergent contributions in the non-minimal gauges do not vanish off shell, as opposed to the minimal gauge.

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I. L. Buchbinder, E. A. Ivanov, B. S. Merzlikin, K. V. Stepanyantz. 2019-07-29. On gauge dependence of the one-loop divergences in $6D$, ${\cal N} = (1,0)$ and ${\cal N} = (1,1)$ SYM theories. https://doi.org/10.1016/j.physletb.2019.134957

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