01436nas a2200145   4500008004100000245008000041210006900121260001000190520096800200100002001168700002401188700002401212700001801236856003601254       2013                        en  d00aN=2 gauge theories on toric singularities, blow-up formulae and  W-algebrae0 aN2 gauge theories on toric singularities blowup formulae and Wal  bSISSA3 aWe compute the Nekrasov partition function of gauge theories on the\r\n(resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We\r\ndiscuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2\r\n\\to 0 limit along with its modular properties and how to derive them from the\r\nM-theory perspective. On the two-dimensional conformal field theory side, our\r\nresults can be interpreted in terms of representations of the direct sum of\r\nHeisenberg plus W_N-algebrae with suitable central charges, which can be\r\ncomputed from the fan of the resolved toric variety.We provide a check of this\r\ncorrespondence by computing the central charge of the two-dimensional theory\r\nfrom the anomaly polynomial of M5-brane theory. Upon using the AGT\r\ncorrespondence our results provide a candidate for the conformal blocks and\r\nthree-point functions of a class of the two-dimensional CFTs which includes\r\nparafermionic theories.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagi, Futoshi  uhttp://hdl.handle.net/1963/657700922nas a2200133   4500008004100000245007400041210006900115260001000184520049000194100002000684700002400704700002400728856003600752       2012                        en  d00aGauge Theories on ALE Space and Super Liouville Correlation Functions0 aGauge Theories on ALE Space and Super Liouville Correlation Func  bSISSA3 aWe present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/430500994nas a2200133   4500008004100000245003100041210003100072260001000103520064300113100002000756700002400776700002400800856003600824       2012                        en  d00aWild quiver gauge theories0 aWild quiver gauge theories  bSISSA3 a<p>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.</p>1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/518401134nas a2200145   4500008004100000245006700041210006700108260001000175520068000185100002000865700002400885700002400909700001900933856003600952       2011                        en  d00aGeneralized matrix models and AGT correspondence at all genera0 aGeneralized matrix models and AGT correspondence at all genera  bSISSA3 aWe 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.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagib, Futoshi  uhttp://hdl.handle.net/1963/656800632nas a2200133   4500008004100000245007400041210006900115260001000184520020000194100002000394700002400414700002400438856003600462       2011                        en  d00aInstantons on ALE spaces and Super Liouville Conformal Field Theories0 aInstantons on ALE spaces and Super Liouville Conformal Field The  bSISSA3 aWe 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).1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/426201134nas a2200133   4500008004100000245006000041210005900101260001000160520072600170100002000896700002400916700002400940856003600964       2011                        en  d00aQuantum Hitchin Systems via beta-deformed Matrix Models0 aQuantum Hitchin Systems via betadeformed Matrix Models  bSISSA3 a<p>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.</p>1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro  uhttp://hdl.handle.net/1963/4181