On the two-loop divergences of the 2-point hypermultiplet supergraphs for $6D$, ${\cal N} = (1,1)$ SYM theory

TL;DR

This paper investigates two-loop divergences in 6D, N=(1,1) supersymmetric Yang-Mills theory within harmonic superspace, demonstrating that hypermultiplet sector divergences cancel out off shell.

Contribution

It provides a detailed analysis of two-loop divergences in the hypermultiplet sector and proves their cancellation off shell in 6D, N=(1,1) SYM theory.

Findings

Two-loop divergences in hypermultiplet sector vanish off shell.

Use of superfield background field method in harmonic superspace.

Confirmation of divergence cancellation in 6D, N=(1,1) SYM.

Abstract

We consider $6D$, ${\cal N}=(1,1)$ supersymmetric Yang-Mills theory formulated in ${\cal N}=(1,0)$ harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the ${\cal N}=(1,0)$ superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.