Superconformal index with surface defects for class ${\mathcal{S}}_k$

Abstract

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.

26 pages

References in corpus (6)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Charting Class ${\mathcal{S}}_k$ Territory
• Chiral theories of class S
• N=1 theories of class S_k
• Heterotic Surface Defects and Dualities from 2d/4d Indices

Cited by in corpus (11)

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• A slow review of the AGT correspondence
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• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
• Surface Operators from M-strings
• Deconstructing Defects
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians