On the description of surface operators in N=2* super Yang-Mills

TL;DR

This paper explores the extension of 2D conformal field theory descriptions of surface operators in N=2* super Yang-Mills, focusing on non-fundamental operators and their relation to affine symmetry and vertex operators.

Contribution

It proposes a framework connecting non-fundamental surface operators in N=2* SYM to vertex operators in 2D CFTs with reduced affine symmetry.

Findings

Non-fundamental surface operators correspond to single vertex operators in 2D CFTs.

The central charge of the CFT is related to the singularity type of the surface operator.

The analysis extends the AGT correspondence to a broader class of surface operators.

Abstract

In Ref. [arXiv:1005.4469], Alday and Tachikawa observed that the Nekrasov partition function of N=2 SU(2) superconformal gauge theories in the presence of fundamental surface operators can be associated to conformal blocks of a 2D CFT with affine sl(2) symmetry. This can be interpreted as the insertion of a fundamental surface operator changing the conformal symmetry from the Virasoro symmetry discovered in [arXiv:0906.3219] to the affine Kac-Moody symmetry. A natural question arises as to how such a 2D CFT description can be extended to the case of non-fundamental surface operators. Motivated by this question, we review the results of Refs. [arXiv:0706.1030] and [arXiv:0803.2099] and put them together to suggest a way to address the problem: It follows from this analysis that the expectation value of a non-fundamental surface operator in the SU(2) N=2* super Yang-Mills theory would be in correspondence with the expectation value of a single vertex operator in a two-dimensional CFT with reduced affine symmetry and whose central charge is parameterized by the integer number that labels the type of singularity of the surface operator.