Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superconformal index with surface defects for class ${\cal S}_k$   We study surface defects in 4d $\mathcal{N}=1$ $SU(N)$ superconformal gauge
theories of class $\mathcal{S}_k$ obtained from the 6d (1,0) theories of type
$A_{N-1}$, which are worldvolume theories on $N$ M5-branes at
$\mathbb{C}^2/\mathbb{Z}_k$ singularities, compactified on Riemann surfaces
with punctures. 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 $\mathcal{N}=(0,2)$ 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 $\mathcal{S}_{k}$ theories by obtaining several eigenfunctions
and eigenvalues of the difference operators that capture the surface defects
and checking their relation.

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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
2
The categories of this paper are: math
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat