A bstract We evaluate the superconformal index of 4d N N = 4 SYM with gauge algebra so (2 N c + 1) in the Cardy-like limit. We then study the relation with the results obtained for the S-dual usp (2 N c ), discussing the fate of S-duality in different regions of charges. We find that S-duality is preserved thanks to a non-trivial integral identity that relates the three sphere partition functions of pure 3d Chern-Simons gauge theories.
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Amariti et al. (2024) studied this question.
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