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

We consider $6D$, $\mathcal{N}=(1,1)$ supersymmetric Yang-Mills theory formulated in $\mathcal{N}=(1,0)$ 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.