Gauge theory non-local operators from two dimensional conformal field theories

by Filippo Passerini (Humboldt-Universität zu Berlin)

Tuesday 14 Sept 2010, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

The partition function of a family of four dimensional N=2 gauge theories has been related by Alday, Gaiotto and Tachikawa (AGT) to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A1 conformal Toda field theory, i.e. Liouville theory. In this seminar I will discuss how the AGT proposal is modified when the gauge theories include non-local operators. I will focus in particular on Wilson loop operators and a certain type of surface operators in SU(N) N=2 gauge theories. For the case of the surface operator, I will show that the relevant two dimensional field theory is a conformal theory with SL(N) affine algebra. This result generalizes the recent result by Alday and Tachikawa that relates SU(2) gauge theories with surface operators to SL(2) affine algebras.