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arXiv · 1205.4230

A 5d/3d duality from relativistic integrable system

Heng-Yu Chen·Timothy J. Hollowood·Peng Zhao
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Abstract

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.

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Heng-Yu Chen, Timothy J. Hollowood, Peng Zhao. 2012-07-23. A 5d/3d duality from relativistic integrable system. https://doi.org/10.1007/jhep07(2012)139

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