00979nas a2200109 4500008004300000245005400043210005100097520064100148100002000789700002400809856003600833 2010 en_Ud 00aHitchin systems, N=2 gauge theories and W-gravity0 aHitchin systems N2 gauge theories and Wgravity3 aWe propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE\\\'s obtaining that Nekrasov\\\'s partition function satisfies W-geometry constraints.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/3831