### Surface defects of class $S_k$ theories as transfer matrices of integrable lattice models

We compute the index of class $S_k$ theories with surface defects labeled by symmetric representations of SU(N). The index of the theory deformed by surface defects is related to the index of the undeformed theory by an action of a family of difference operators (=defect operators). These defect operators can be shown to correspond to transfer matrices constructed from L-operators obtained by reduction of the most general known solution to the rank one Yang--Baxter equation (i.e. the BSDS R-matrix). For rank one theories it is possible to extract directly the L-operator, which corresponds to a fundamental building block of the class $S_k$ quiver (reduced by an appropriate Higgsing leading to the surface defect in the IR). This result is based on properly interpreting the work arXiv:1412.3383 from the gauge theory perspective.

**Tuesday, 6 November 2018, 14:30, Aula Wataghin**