On two-loop divergences of effective action in 6D, $$ \mathcal{N} $$ = (1, 1) SYM theory

Abstract

We study the off-shell structure of the two-loop effective action in 6D,$$ \mathcal{N} $$ N = (1, 1) supersymmetric gauge theories formulated in $$ \mathcal{N} $$ N = (1, 0) harmonic superspace. The off-shell effective action involving all fields of 6D,$$ \mathcal{N} $$ N = (1, 1) supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest $$ \mathcal{N} $$ N = (1, 0) supersymmetry. We analyze the off-shell divergences dependent on both gauge and hypermultiplet superfields and argue that the gauge invariance of the divergences is consistent with the non-locality in harmonics. The two-loop contributions to the effective action are given by harmonic supergraphs with the background gauge and hypermultiplet superfields. The procedure is developed to operate with the harmonic-dependent superpropagators in the two-loop supergraphs within the superfield dimensional regularization. We explicitly calculate the gauge and the hypermultiplet-mixed divergences as the coefficients of $$ \frac{1}{\varepsilon^2} $$ 1 ε 2 and demonstrate that the corresponding expressions are non-local in harmonics.