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

Abstract

We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/Γin terms of blow-up formulae. We discuss the expansion of the partition function in the ε_1,ε_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.

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

References in corpus (4)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Instanton on toric singularities and black hole countings
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

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