We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C2/Γ in terms of blow-up formulae. We discuss the expansion of the partition function in the e1,e2 → 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.

N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae / Bonelli, G.; Maruyoshi, K.; Tanzini, A.; Yagi, F.. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2013:1(2013), pp. 1-30. [10.1007/JHEP01(2013)014]

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

Bonelli, G.;Tanzini, A.;
2013-01-01

Abstract

We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C2/Γ in terms of blow-up formulae. We discuss the expansion of the partition function in the e1,e2 → 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.
2013
2013
1
1
30
014
https://doi.org/10.1007/JHEP01(2013)014
Bonelli, G.; Maruyoshi, K.; Tanzini, A.; Yagi, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12779
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