One-loop divergences in the 6D, N=(1,0) abelian gauge theory

TL;DR

This paper analyzes one-loop divergences in a 6D N=(1,0) abelian gauge theory using harmonic superspace, revealing finiteness in the gauge sector but UV divergences in the mixed gauge-hypermultiplet sector.

Contribution

It provides a detailed superfield calculation of divergences in 6D N=(1,0) supersymmetric gauge theory, highlighting the UV divergence in the mixed sector.

Findings

Gauge sector is one-loop finite on-shell.

Mixed sector exhibits unavoidable UV divergences.

Explicit superfield computations of divergences are presented.

Abstract

We consider, in the harmonic superspace approach, the six-dimensional N=(1,0) supersymmetric model of abelian gauge multiplet coupled to a hypermultiplet. The superficial degree of divergence is evaluated and the structure of possible one-loop divergences is analyzed. Using the superfield proper-time and background-field technique, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. The corresponding counterterms contain the purely gauge multiplet contribution together with the mixed contributions of the gauge multiplet and hypermultiplet. We show that the theory is on-shell one-loop finite in the gauge multiplet sector in agreement with the results of [1]. The divergences in the mixed sector cannot be eliminated by any field redefinition, implying the theory to be UV divergent at one loop.