On the two-loop divergences in 6D, ${\cal N}=(1,1)$ SYM theory

TL;DR

This paper investigates two-loop divergences in 6D, ${ m N}=(1,1)$ supersymmetric Yang-Mills theory, showing that divergences are proportional to equations of motion and vanish on shell, with detailed supergraph analysis.

Contribution

It provides a detailed superfield background field analysis of two-loop divergences in 6D, ${ m N}=(1,1)$ SYM, demonstrating divergence cancellation on shell and exploring divergence structures.

Findings

Only one of four supergraphs diverges off shell.

Divergences are proportional to classical equations of motion.

Divergences vanish on shell.

Abstract

We continue studying $6D, {\cal N}=(1,1)$ supersymmetric Yang-Mills (SYM) theory in the ${\cal N}=(1,0)$ harmonic superspace formulation. Using the superfield background field method we explore the two-loop divergencies of the effective action in the gauge multiplet sector. It is explicitly demonstrated that among four two-loop background-field dependent supergraphs contributing to the effective action, only one diverges off shell. It is also shown that the divergences are proportional to the superfield classical equations of motion and hence vanish on shell. Besides, we have analyzed a possible structure of the two-loop divergences on general gauge and hypermultiplet background.