Supergraph analysis of the one-loop divergences in 6D, $N=(1,0)$ and $N=(1,1)$ gauge theories

We study the one-loop effective action for 6D, $N=(1,0)$ supersymmetric Yang–Mills (SYM) theory with hypermultiplets and 6D, $N=(1,1)$ SYM theory as a subclass of the former, using the off-shell formulation of these theories in 6D, $N=(1,0)$ harmonic superspace. We develop the corresponding supergraph technique and apply it to compute the one-loop divergences in the background field method ensuring the manifest gauge invariance. We calculate the two-point Green functions of the gauge superfield and the hypermultiplet, as well as the three-point gauge-hypermultipet Green function. Using these Green functions and exploiting gauge invariance of the theory, we find the full set of the off-shell one-loop divergent contributions, including the logarithmic and power ones. Our results precisely match with those obtained earlier in [1], [2] within the proper time superfield method.