2013/01/31 by Juan Pablo Babaro, Gaston Giribet
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0217732313300036
published as Mod. Phys. Lett. A28 (2013) 1330003 · 15 pages. v2 typo corrected, comments added. Invited article for MPLA
arxiv created 2013/02/12 · arxiv updated 2013/10/22
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.