We study $N=2$ supersymmetric $SU(2)$ gauge theories coupled to non-Lagrangian superconformal field theories induced by compactifying the six dimensional $A_1 (2,0)$ theory on Riemann surfaces with irregular punctures. These are naturally associated to Hitchin systems with wild ramification whose spectral curves provide the relevant Seiberg-Witten geometries. We propose that the prepotential of these gauge theories on the Omega-background can be obtained from the corresponding irregular conformal blocks on the Riemann surfaces via a generalization of the coherent state construction to the case of higher order singularities.

PB - SISSA UR - http://hdl.handle.net/1963/5184 N1 - 34 pages U1 - 4999 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - JOUR T1 - Generalized matrix models and AGT correspondence at all genera JF - JHEP, Volume 2011, Issue 7, 2011, Article number055 Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini A1 - Futoshi Yagib AB - We study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera. PB - SISSA UR - http://hdl.handle.net/1963/6568 N1 - This version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055 U1 - 6530 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Instantons on ALE spaces and Super Liouville Conformal Field Theories Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB - We provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2). PB - SISSA UR - http://hdl.handle.net/1963/4262 N1 - 10 pages U1 - 3987 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER - TY - RPRT T1 - Quantum Hitchin Systems via beta-deformed Matrix Models Y1 - 2011 A1 - Giulio Bonelli A1 - Kazunobu Maruyoshi A1 - Alessandro Tanzini AB -We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the epsilon1-deformation of the chiral observables of the corresponding N=2 four ndimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

PB - SISSA UR - http://hdl.handle.net/1963/4181 N1 - 29 pages; v2. refs. added and typos corrected U1 - 3904 U2 - Physics U3 - Elementary Particle Theory U4 - -1 ER -