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On S-duality of 5d super Yang-Mills on S 1

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Abstract

We study a duality of 5d maximally supersymmetric Yang-Mills on S 1, which exchanges the tower of Kaluza-Klein W-bosons and the tower of instantonic monopoles. This duality maps a non-simply-laced gauge theory to a simply-laced gauge theory twisted by an outer automorphism around S 1, and is closely related to the Langlands dual of affine Lie algebras. We also discuss how this S-duality is implemented in terms of 6d \(\mathcal{N}\) = (2, 0) theory. This is straightforward except for the 6d theory of type SU(2n + 1) with \({\mathbb{Z}_2}\) outer-automorphism twist, for which a few new properties are deduced. For example, this 6d theory, when reduced on an S 1 with \({\mathbb{Z}_2}\) twist, gives 5d USp(2n) theory with nontrivial discrete 5d theta angle.

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  1. IPMU, University of Tokyo, Kashiwa, Chiba, 277-8583, Japan

    Yuji Tachikawa

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Tachikawa, Y. On S-duality of 5d super Yang-Mills on S 1 . J. High Energ. Phys. 2011, 123 (2011). https://doi.org/10.1007/JHEP11(2011)123

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