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arXiv · 1011.0289

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

Niclas Wyllard
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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.

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Niclas Wyllard. 2011-03-12. W-algebras and surface operators in N=2 gauge theories. https://doi.org/10.1088/1751-8113%2F44%2F15%2F155401

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