Surface defects as transfer matrices

Abstract

The supersymmetric index of the 4d $\mathcal{N}=1$ theory realized by a brane tiling coincides with the partition function of an integrable 2d lattice model. We argue that a class of half-BPS surface defects in brane tiling models are represented on the lattice model side by transfer matrices constructed from L-operators. For the simplest surface defects in theories with $\mathrm{SU}(2)$ flavor groups, we identify the relevant L-operator as that discovered by Sklyanin in the context of the eight-vertex model. We verify this identification by computing the indices of class-$\mathcal{S}$ and -${\mathcal{S}}_k$ theories in the presence of the surface defects.

58 pages. v2: minor changes, references added. v3: published version

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Cited by in corpus (16)

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• A slow review of the AGT correspondence
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• Superspin chains from superstring theory
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• Weakly coupled conformal manifolds in 4d
• 't Hooft lines of ADE-type and Topological Quivers
• Lens elliptic gamma function solution of the Yang-Baxter equation at roots of unity
• Surface Operators from M-strings
• Branes and integrable lattice models
• Lax Operator and superspin chains from 4D CS gauge theory
• Integrable 3D lattice model in M-theory
• An infrared bootstrap of the Schur index with surface defects
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• Aspects of 4d supersymmetric dynamics and geometry