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

Abstract

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, $\mathcal{N}=(1,0)$ 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 $\mathcal{N}=(1,0)$ 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.

18 pages, 1 figure, final version accepted for publication in JHEP