The renormalization structure of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory

TL;DR

This paper analyzes the renormalization structure of a six-dimensional supersymmetric gauge theory with higher derivatives, demonstrating its renormalizability and calculating the one-loop divergences within a manifestly supersymmetric framework.

Contribution

It provides a detailed superfield background method analysis of the 6D, ${\cal N}=(1,0)$ higher-derivative gauge theory, showing its renormalizability and explicit one-loop divergence calculations.

Findings

Superficial degree of divergence is loop-independent.

Counterterms can be removed by coupling constant renormalization.

Hypermultiplet sector divergences are absent at all loops.

Abstract

We consider the harmonic superspace formulation of higher-derivative $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory and its minimal coupling to a hypermultiplet. In components, the kinetic term for the gauge field in such a theory involves four space-time derivatives.The theory is quantized in the framework of the superfield background method ensuring manifest $6D$, ${\cal N}=(1,0)$ supersymmetry and the classical gauge invariance of the quantum effective action. We evaluate the superficial degree of divergence and prove it to be independent of the number of loops. Using the regularization by dimensional reduction, we find possible counterterms and show that they can be removed by the coupling constant renormalization for any number of loops, while the divergences in the hypermultiplet sector are absent at all. Assuming that the deviation of the gauge-fixing term from that in the Feynman gauge is small, we explicitly calculate the divergent part of the one-loop effective action in the lowest order in this deviation. In the approximation considered, the result is independent of the gauge-fixing parameter and agrees with the earlier calculation for the theory without a hypermultiplet.