Abstract
We study the off-shell structure of the two-loop effective action in 6D, \( \mathcal{N} \) = (1, 1) supersymmetric gauge theories formulated in \( \mathcal{N} \) = (1, 0) harmonic superspace. The off-shell effective action involving all fields of 6D, \( \mathcal{N} \) = (1, 1) supermultiplet is constructed by the harmonic superfield background field method, which ensures both manifest gauge covariance and manifest \( \mathcal{N} \) = (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 \( \frac{1}{\varepsilon^2} \) and demonstrate that the corresponding expressions are non-local in harmonics.
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Acknowledgments
Work of I.L.B., E.A.I. and K.V.S. was supported by Russian Scientific Foundation, project No 21-12-00129. Work of B.S.M was supported in part by the Ministry of Education of the Russian Federation, project QZOY-2023-0003.
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Buchbinder, I.L., Ivanov, E.A., Merzlikin, B.S. et al. On two-loop divergences of effective action in 6D, \( \mathcal{N} \) = (1, 1) SYM theory. J. High Energ. Phys. 2023, 89 (2023). https://doi.org/10.1007/JHEP05(2023)089
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DOI: https://doi.org/10.1007/JHEP05(2023)089