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

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.