W-algebras and surface operators in N=2 gauge theories

Abstract

A general class of W-algebras can be constructed from the affine sl(N) algebra by (quantum) Drinfeld-Sokolov reduction and are classified by partitions of N. Surface operators in an N=2 SU(N) 4d gauge theory are also classified by partitions of N. We argue that instanton partition functions of N=2 gauge theories in the presence of a surface operator can also be computed from the corresponding W-algebra. We test this proposal by analysing the Polyakov-Bershadsky W_3^(2) algebra obtaining results that are in agreement with the known partition functions for SU(3) gauge theories with a so called simple surface operator. As a byproduct, our proposal implies relations between the W_3^(2) and W_3 algebras.

arXiv comment16 pages. v2: minor changes. v3: added two references

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Cited by in corpus (17)

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• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• Thermodynamics of higher spin black holes in 3D
• M2-brane surface operators and gauge theory dualities in Toda
• A slow review of the AGT correspondence
• Holomorphic blocks and the 5d AGT correspondence
• Intersecting Surface Defects and Two-Dimensional CFT
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• N=2 SUSY gauge theories on S^4
• Supergroup - extended super Liouville correspondence
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• On the six-dimensional origin of the AGT correspondence
• (de)Tails of Toda CFT
• Correspondences among CFTs with different W-algebra symmetry
• Orbifolds, Defects and Sphere Partition Function
• Affine Laumon spaces and iterated W-algebras