$ mathcal{N}=2 $ gauge theories on toric singularities, blow-up formulae and W-algebrae
$ mathcal{N}=2 $ gauge theories on toric singularities, blow-up formulae and W-algebrae
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$ mathcal{N}=2 $ 关于环面奇点、爆炸公式和 W 代数的规范理论
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
F. Yagi
中科院分区：
文献类型：
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作者：
G. Bonelli;K. Maruyoshi;A. Tanzini;F. Yagi
本文计算了（分解的）复曲面奇点${mathbb{C}}^2} left/ {varGamma }上规范理论的Nekrasov配分函数
right.} $在blow-up公式中。我们讨论了配分函数在n = 1，n = 2 → 0极限的展开及其模性质，以及如何从M-理论的角度推导它们。在二维共形场论方面，我们的结果可以解释为海森堡加WN-代数的直和与适当的中心电荷，这可以从解决复曲面品种的风扇计算的表示。我们提供了一个检查这种对应关系的计算中心电荷的二维理论从异常多项式的M5膜理论。在使用AGT对应，我们的结果提供了一个候选人的共形块和三点函数的一类二维CFTs，其中包括parafermionic理论。
A bstractWe compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities $ {{{{{mathbb{C}}^2}}} left/ {varGamma }
ight.} $ in terms of blow-up formulae. We discuss the expansion of the partition function in the ϵ1, ϵ2 → 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 WN-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.