  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.
