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.
Highlights
The study of quantum aspects of the higher-dimensional supersymmetric gauge field theories attracts a wide interest for a long time, mainly because of their use for the low-energy description of diverse sectors of superstring theory
We show that the gauge dependence of the divergences vanishes for the background superfields satisfying the classical equations of motion
We considered the general six-dimensional N = (1, 0) supersymmetric gauge theory in the harmonic superspace formulation and studied the dependence of the one-loop divergences on the gauge-fixing parameter
Summary
The study of quantum aspects of the higher-dimensional supersymmetric gauge field theories attracts a wide interest for a long time, mainly because of their use for the low-energy description of diverse sectors of superstring theory (see, e.g., [1, 2]). The present paper generalizes this study to the generic non-abelian N = (1, 0) SYM theory interacting with a set of hypermultiplets in an arbitrary representation of the gauge group. [18,19,20,21,22] was carried out in the framework of the harmonic superfield background field method, which ensures both the classical gauge invariance and N = (1, 0) supersymmetry as manifest symmetries This method was earlier developed for the minimal gauge only. 3 we develop the background superfield method with the gauge-fixing term containing an arbitrary real parameter and derive the formal expression for the corresponding one-loop effective action.
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