One-loop divergences in the six-dimensional $\cal{N}=(1,0)$ hypermultiplet self-coupling model

TL;DR

This paper analyzes the one-loop divergences in a six-dimensional supersymmetric hypermultiplet model with self-coupling, revealing non-vanishing divergences even on-shell, using harmonic superspace techniques.

Contribution

It introduces a method to compute gauge-invariant one-loop divergences in six-dimensional $ abla$ supersymmetric models with arbitrary self-coupling.

Findings

One-loop divergences do not vanish even on-shell.

Divergences are expressed as gauge-invariant functions of the gauge multiplet.

Technique is applicable to four-dimensional hypermultiplet models.

Abstract

We study the six-dimensional $\cal{N}=(1,0)$ supersymmetric hypermultiplet model with arbitrary self-coupling. The model is considered in the external classical gauge superfield background. Using the harmonic superspace formulation we study the one-loop effective action of the model. We calculate the one-loop divergences in the theory as a gauge-invariant function of the external gauge multiplet. We demonstrate that the one-loop divergences in the theory do not vanish even in the case of on-shell hypermultiplet background. We briefly discuss an application of the developed technique to the hypermultiplet model in four dimensions.