Using localization techniques, Pestun has shown how to reduce certain quantum field theory path integrals to finite-dimensional matrix integrals. In this way, the expectation value of certain operators in the gauge theory is equivalent to the expectation value of observables in the associated matrix model. In this talk, Pestun's matrix model is used to compute the expectation value of the circular Wilson loop in N = 2 SuperConformal QCD, in the weak and strong coupling regime. At weak coupling, we define a perturbative scheme that permits to compute the Wilson loop at arbitrary high number of loops. At strong coupling, our computation carries information about the string theory dual of the SuperConformal QCD, that is not known yet. In particular, our results indicate that the string tension in the dual string theory scales as the logarithm of the gauge theory 't Hooft coupling.

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.