Superconformal index with surface defects for class Sk

We study surface defects in 4d N = 1 SU (N) superconformal gauge theories of class S-k obtained from the 6d (1,0) theories of type A(N-1), which are worldvolume theories on N M5-branes at C-2/Z(k) singularities, compactified on Riemann surfaces with punctures. We evaluate the superconformal indices with surface defects for the orbifold of linear quiver gauge theories by two methods. First we apply a method based on Riemann surface description and obtain the superconformal index of the theories in the presence of surface defects labelled by arbitrary symmetric representations of su(N). Then we propose another description for the same surface defects, which involves 4d-2d coupled systems, by identifying which 2d N = (0, 2) theories should be coupled. We compute the index of the 4d-2d systems and reproduce the results obtained from the first method. Finally we study the 2d TQFT structure of the index for class S-k theories by obtaining several eigenfunctions and eigenvalues of the difference operators that capture the surface defects and checking their relation. (C) 2020 The Author(s). Published by Elsevier B.V.

Automated summary

Surface defects in 4d N = 1 SU (N) superconformal gauge theories of class S-k, obtained from 6d (1,0) theories of type A(N-1), are studied using two methods to evaluate the superconformal indices. The index of theories with surface defects labeled by arbitrary symmetric representations of su(N) is obtained through a Riemann surface description, while another description involving 4d-2d coupled systems is proposed to compute the index and reproduce the results. The 2d TQFT structure of the index for class S-k theories is studied by obtaining eigenfunctions and eigenvalues of the difference operators capturing the surface defects and checking their relation.