New Integrable Models from the Gauge/YBE Correspondence

Abstract

We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of a large class of SU(N) quiver gauge theories with the partition function of 2d classical integrable spin models. The integrability of the model (star-star relation) is equivalent with the invariance of the index under the Seiberg duality. Our solution to the Yang-Baxter equation is one of the most general known in the literature, and reproduces a number of known integrable models. Our analysis identifies the Yang-Baxter equation with a particular duality (called the Yang-Baxter duality) between two 4d N=1 supersymmetric quiver gauge theories. This suggests that the integrability goes beyond 4d lens indices and can be extended to the full physical equivalence among the IR fixed points.

20 pages, 9 figures

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• Seiberg Duality in Chern-Simons Theory
• Brane Tilings
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Cited by in corpus (25)

• (0,2) Trialities
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• The supersymmetric index in four dimensions
• Aspects of Defects in 3d-3d Correspondence
• New solutions of the star-triangle relation with discrete and continuous spin variables
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory
• Quiver gauge theories and integrable lattice models
• Integrability from 2d N=(2,2) Dualities
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Surface defects as transfer matrices
• T-Reflection
• Quantum line operators from Lax pairs
• Integrable lattice spin models from supersymmetric dualities
• Elliptic modular double and 4d partition functions
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Branes and integrable lattice models
• Extended Z-invariance for integrable vector and face models and multi-component integrable quad equations
• Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• Exactly solved models on planar graphs with vertices in ${\mathbb{Z}}^3$
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations