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.

16 pages. v2: minor changes. v3: added two references

References in corpus (5)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Correlation functions in conformal Toda field theory I
• The Power of Nekrasov Functions
• Gauge Theory Wilson Loops and Conformal Toda Field Theory

Cited by in corpus (4)

• 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
• (de)Tails of Toda CFT
• Affine Laumon spaces and iterated W-algebras