Browsing by Author "Maruyoshi, Kazunobu"
Now showing 1 - 7 of 7
Results Per Page
Sort Options
Item Instantons on ALE spaces and Super Liouville Conformal Field Theories(SISSA, 2011-06-13) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Physics; Mathematics; Elementary Particle Theory; Mathematical PhysicsWe provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Item Instantons on ALE spaces and Super Liouville Conformal Field Theories(SISSA, 2011-06-13) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; MathematicsWe provide evidence that the conformal blocks of N=1 super Liouville conformal field theory are described in terms of the SU(2) Nekrasov partition function on the ALE space O_{P^1}(-2).Item N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae(SISSA, 2013-02-05) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Yagi, Futoshi; MathematicsWe compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \epsilon_1,\epsilon_2 \to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety.We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.Item N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae(SISSA, 2012-08-03) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Yagi, Futoshi; Physics; Mathematics; Elementary Particle Theory; Mathematical PhysicsWe compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \epsilon_1,\epsilon_2 \to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety. We provide a check of this correspondence by computing the central charge of the two-dimensional theory from the anomaly polynomial of M5-brane theory. Upon using the AGT correspondence our results provide a candidate for the conformal blocks and three-point functions of a class of the two-dimensional CFTs which includes parafermionic theories.Item Quantum Hitchin Systems via beta-deformed Matrix Models(SISSA, 2011-05-17) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; MathematicsWe 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 dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.Item Quantum Hitchin Systems via beta-deformed Matrix Models(SISSA, 2011-04-20) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; Physics; Mathematics; Elementary Particle Theory; Mathematical PhysicsWe 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 dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.Item Wild Quiver Gauge Theories(SISSA, 2011-12-15) Bonelli, Giulio; Maruyoshi, Kazunobu; Tanzini, Alessandro; MathematicsWe 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.