Surface defects as transfer matrices

Kazunobu Maruyoshi, Junya Yagi

Published 2016-06-03Version 1

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 propose 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 defect 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 our proposal by computing the indices of class-$\mathcal{S}$ and -$\mathcal{S}_k$ theories in the presence of the surface defect.