Quiver gauge theories and integrable lattice models

Abstract

We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N}=1$ theories known as brane box and brane tilling models, 3d $\mathcal{N}=2$ and 2d $\mathcal{N}=(2,2)$ theories obtained from them by compactification, and 2d $\mathcal{N}=(0,2)$ theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.

46 pages. v2: minor changes and corrections; v3: minor changes and corrections, references added, published version; v4: typos corrected, a reference corrected

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• Brane Tilings
• Brane Tilings and Their Applications
• Quivers, YBE and 3-manifolds
• The star-triangle relation and 3d superconformal indices
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Cited by in corpus (23)

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• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Surface defects as transfer matrices
• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
• Integrable lattice spin models from supersymmetric dualities
• Quantum line operators from Lax pairs
• Elliptic modular double and 4d partition functions
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Branes and integrable lattice models
• Integrable 3D lattice model in M-theory
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities
• Superconformal indices, Seiberg dualities and special functions
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• 2d dualities from 4d
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Tetrahedron duality