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.
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
