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

DOI number:10.1007/jhep01(2013)014

Journal:Journal of High Energy Physics

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.

Note:The preprint version is available at https://arxiv.org/abs/1208.0790

Co-author:Giulio Bonelli,Kazunobu Maruyoshi,Alessandro Tanzini,Futoshi Yagi

Indexed by:SCI

Discipline:Science

Volume:01(2013)

Issue:014

Translation or Not:no

Date of Publication:2013-01-02

Included Journals:SCI

Links to published journals:https://doi.org/10.1007/jhep01(2013)014