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arXiv · 1110.0531

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

Yuji Tachikawa
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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 N=(2,0) theory. This is straightforward except for the 6d theory of type SU(2n+1) with 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 Z_2 twist, gives 5d USp(2n) theory with nontrivial discrete 5d theta angle.

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Yuji Tachikawa. 2011-11-25. On S-duality of 5d super Yang-Mills on S^1. https://doi.org/10.1007/jhep11(2011)123

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