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/1963/383100967nas a2200109   4500008004300000245005100043210004700094520063600141100002000777700002400797856003600821       2007                        en_Ud  00aThe holomorphic anomaly for open string moduli0 aholomorphic anomaly for open string moduli3 aWe complete the holomorphic anomaly equations for topological strings with their dependence on open moduli. We obtain the complete system by standard path integral arguments generalizing the analysis of BCOV (Commun. Math. Phys. 165 (1994) 311) to strings with boundaries. We study both the anti-holomorphic dependence on open moduli and on closed moduli in presence of Wilson lines. By providing the compactification a\\\' la Deligne-Mumford of the moduli space of Riemann surfaces with boundaries, we show that the open holomorphic anomaly equations are structured on the (real codimension one) boundary components of this space.1 aBonelli, Giulio1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/2113