One-loop divergences in 6D, mathcal{N} = (1, 0) SYM theory

Abstract

We consider, in the harmonic superspace approach, the six-dimensional mathcal{N} = (1, 0) supersymmetric Yang-Mills gauge multiplet minimally coupled to a hypermultiplet in an arbitrary representation of the gauge group. Using the superfield proper-time and background-field techniques, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. We demonstrate that in the particular case of mathcal{N} = (1, 1) SYM theory, which corresponds to the hypermultiplet in the adjoint representation, all one-loop divergencies vanish, so that mathcal{N} = (1, 1) SYM theory is one-loop finite off shell.