SISSA Open Science

N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae

Show simple item record Bonelli, Giulio Maruyoshi, Kazunobu Tanzini, Alessandro Yagi, Futoshi 2013-04-04T10:56:22Z 2013-04-04T10:56:22Z 2013-02-05
dc.description 33 pages, 1 figure; v2: discussions on U(1) gauge theory and Frenkel-Kac construction have been added in section 5.1, and typos corrected; v3: published version; v4: typos corrected en_US
dc.description.abstract We 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. en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries arXiv:1208.0790;
dc.relation.ispartofseries SISSA preprint;23/2012/EP-FM
dc.rights SISSA en_US
dc.title N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae en_US
dc.type Preprint en_US
dc.miur.area -1 en_US
dc.contributor.area Mathematics en_US

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