Supergraph calculation of one-loop divergences in higher-derivative $6D$ SYM theory

TL;DR

This paper uses harmonic superspace and background superfield methods to compute one-loop divergences in 6D, ${ m N}=(1,0)$ higher-derivative SYM theory, deriving the beta function and confirming previous component results.

Contribution

It introduces a superfield approach to calculate divergences in higher-derivative 6D SYM, simplifying the process and enabling future generalizations.

Findings

Calculated one-loop divergences using harmonic superspace.

Derived the beta function consistent with earlier component calculations.

Confirmed the sign of the beta function depends on the classical action's sign.

Abstract

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and ${\cal N}=(1,0)$ supersymmetric way. We exploit the regularization by dimensional reduction in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant $\beta$-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed {\it a priori}. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.