One-loop finiteness in higher-derivative $6D$, ${\cal N}=(1,0)$ super Yang-Mills -- hypermultiplet system

TL;DR

This paper demonstrates that a six-dimensional higher-derivative $ ext{N}=(1,0)$ super Yang-Mills theory coupled to a hypermultiplet can be made one-loop finite in the gauge superfield sector through a novel non-minimal interaction, preserving supersymmetry and gauge invariance.

Contribution

Introduction of a non-minimal interaction in 6D higher-derivative supersymmetric gauge theory that cancels one-loop divergences, achieving off-shell finiteness in the vector multiplet sector.

Findings

One-loop divergences are canceled in the gauge superfield sector.

The theory remains gauge invariant and supersymmetric after the cancellation.

Explicit verification using background field and supergraph methods confirms finiteness.

Abstract

We employ the harmonic superspace methods to study a six-dimensional $\mathcal{N}=(1,0)$ supersymmetric gauge theory with higher derivatives coupled to a hypermultiplet in the adjoint representation. By introducing a novel non-minimal interaction between the gauge multiplet and the hypermultiplet, we demonstrate that the one-loop divergences in gauge superfield sector, which are present in the conventional formulation, are canceled. The resulting theory is off-shell one-loop finite in this sector, while preserving the gauge invariance and $\mathcal{N}=(1,0)$ supersymmetry. The cancelation mechanism is explicitly verified using both the background field method and the supergraph techniques. Thus, we present an example of the higher-derivative supersymmetric gauge theory in six dimensions which is finite in the vector multiplet sector.