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arXiv · 1606.01041

Surface defects as transfer matrices

Kazunobu Maruyoshi·Junya Yagi
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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.

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Kazunobu Maruyoshi, Junya Yagi. 2016-06-03. Surface defects as transfer matrices. https://doi.org/10.1093/ptep/ptw151

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