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

TL;DR

This paper calculates one-loop divergences in 6D N=(1,0) supersymmetric Yang-Mills theory using harmonic superspace, showing that N=(1,1) case is finite at one loop off shell.

Contribution

It provides a detailed superfield computation of divergences in 6D N=(1,0) SYM with hypermultiplets, demonstrating finiteness of N=(1,1) SYM at one loop.

Findings

All one-loop divergences vanish in N=(1,1) SYM.

Divergences depend on gauge multiplet and hypermultiplet interactions.

The off-shell finiteness of N=(1,1) SYM is established.

Abstract

We consider, in the harmonic superspace approach, the six-dimensional 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 N=(1,1) SYM theory, which corresponds to the hypermultiplet in the adjoint representation, all one-loop divergencies vanish, so that N=(1,1) SYM theory is one-loop finite {\it off shell}.