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We study the gauge dependence of the one-loop effective action for theabelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated inharmonic superspace. We introduce the superfield $\xi$-gauge, construct thecorresponding gauge superfield propagator, and calculate the one-loop two-andthree-point Green functions with two external hypermultiplet legs. Wedemonstrate that in the general $\xi$-gauge the two-point Green function of thehypermultiplet is divergent, as opposed to the Feynman gauge $\xi =1$. Thethree-point Green function with two external hypermultiplet legs and one leg ofthe gauge superfield is also divergent. We verified that the Green functionsconsidered satisfy the Ward identity formulated in ${\cal N}=(1,0)$ harmonicsuperspace and that their gauge dependence vanishes on shell. Using the resultfor the two- and three-point Green functions and arguments based on the gaugeinvariance, we present the complete divergent part of the one-loop effectiveaction in the general $\xi$-gauge.

Gauge dependence of the one-loop divergences in $6D$, ${\cal N} = (1,0)$ abelian theory