Browsing by Author "Yagi, Futoshi"
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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.