@article {2013,
	title = {N=2 gauge theories on toric singularities, blow-up formulae and  W-algebrae},
	number = {arXiv:1208.0790;},
	year = {2013},
	note = {33 pages, 1 figure; v2: discussions on U(1) gauge theory and\r\n  Frenkel-Kac construction have been added in section 5.1, and typos corrected;\r\n  v3: published version; v4: typos corrected},
	institution = {SISSA},
	abstract = {We 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.},
	url = {http://hdl.handle.net/1963/6577},
	author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagi}
}
@article {2012,
	title = {Gauge Theories on ALE Space and Super Liouville Correlation Functions},
	journal = {Lett. Math. Phys. 101 (2012) 103-124},
	number = {arXiv:1107.4609v1;},
	year = {2012},
	note = {21 pages},
	publisher = {SISSA},
	abstract = {We 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.},
	doi = {10.1007/s11005-012-0553-x},
	url = {http://hdl.handle.net/1963/4305},
	author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini}
}
@article {2012,
	title = {Wild quiver gauge theories},
	journal = {JHEP 02(2012)031},
	number = {arXiv:1112.1691v1;},
	year = {2012},
	note = {34 pages},
	publisher = {SISSA},
	abstract = {<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>},
	doi = {10.1007/JHEP02(2012)031},
	url = {http://hdl.handle.net/1963/5184},
	author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini}
}
@article {2011,
	title = {Generalized matrix models and AGT correspondence at all genera},
	journal = {JHEP, Volume 2011, Issue 7, 2011, Article number055},
	number = {arXiv:1011.5417;},
	year = {2011},
	note = {This  version is published in : Journal of High Energy Physics, Volume 2011, Issue 7, 2011, Article number055},
	publisher = {SISSA},
	abstract = {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.},
	doi = {10.1007/JHEP07(2011)055},
	url = {http://hdl.handle.net/1963/6568},
	author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini and Futoshi Yagib}
}
@article {2011,
	title = {Instantons on ALE spaces and Super Liouville Conformal Field Theories},
	number = {arXiv:1106.2505v1;},
	year = {2011},
	note = {10 pages},
	institution = {SISSA},
	abstract = {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).},
	url = {http://hdl.handle.net/1963/4262},
	author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini}
}
@article {2011,
	title = {Quantum Hitchin Systems via beta-deformed Matrix Models},
	number = {arXiv:1104.4016v2;},
	year = {2011},
	note = {29 pages; v2. refs. added and typos corrected},
	institution = {SISSA},
	abstract = {<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>},
	url = {http://hdl.handle.net/1963/4181},
	author = {Giulio Bonelli and Kazunobu Maruyoshi and Alessandro Tanzini}
}
