A 5d/3d duality from relativistic integrable system

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.

30 pages, 4 figures. v2: typo corrected, references added

References in corpus (7)

• Notes on SUSY Gauge Theories on Three-Sphere
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Supersymmetric Gauge Theories on the Five-Sphere
• The Omega Deformation From String and M-Theory
• Relating Gauge Theories via Gauge/Bethe Correspondence
• The Dynamics of Chern-Simons Vortices
• Chern-Simons Theory and S-duality

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• Equations on knot polynomials and 3d/5d duality
• An elliptic Virasoro symmetry in 6d
• BPS States in Omega Background and Integrability
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
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• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Quantum integrability from non-simply laced quiver gauge theory
• Gauge origami and quiver W-algebras
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• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Bethe/Gauge Correspondence for linear quiver theories with ABCD gauge symmetry and spin chains
• Solution of quantum integrable systems from quiver gauge theories
• New dimer integrable systems and defects in five dimensional gauge theory
• Defects and type D relativistic Toda lattice for some 5d gauge theories
• Generalized Calogero-Moser system and supergroup gauge origami
• Chiral rings for surface operators in 4d and 5d SQCD