论文标题
衡量紧凑型复曲面的理论
Gauge theories on compact toric manifolds
论文作者
论文摘要
我们计算$ {\ cal n} = 2 $通过epariatiant定位在四维紧凑型孢子歧管上的量规理论的超对称分区功能。结果由Kähler形式的分段常数函数给出，并沿着尺寸对称性增强的墙壁跳跃。此类歧管上的分区函数被写为$ \ Mathbb {c}^2 $的分区函数的残基的总和。通过使用将残基与$ \ Mathbb {C}^2 $分区函数相关联的“抽象二元性”，可以大大简化对这些残基的评估。在特殊情况下，我们的公式计算$ \ mathbb {p}^2 $和$ \ mathbb {f} _n $的$ su（2）$和$ su（3）$ {\ it equivariant} donaldson noffariants，在非等效的限制中，并通过$ coss $ cups $ cupss $ cuss $ cuss $ cupss $ cuss $ cupss $ cupss $ cups $ cupss $ cupss $ cupss $ cups $ cupss $ cupss $ cupss $（最后，我们表明$ u（1）$ dual Connections诱导了对量规耦合的异常依赖，事实证明，该连接满足了$ \ Mathcal {n} = 2 $ holomorphic Anomaly Anomaly artomaly aremaly方程。
We compute the ${\cal N}=2$ supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $\mathbb{C}^2$. The evaluation of these residues is greatly simplified by using an "abstruse duality" that relates the residues at the poles of the one-loop and instanton parts of the $\mathbb{C}^2$ partition function. As particular cases, our formulae compute the $SU(2)$ and $SU(3)$ {\it equivariant} Donaldson invariants of $\mathbb{P}^2$ and $\mathbb{F}_n$ and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the $SU(2)$ case. Finally, we show that the $U(1)$ self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $\mathcal{N}=2$ analog of the $\mathcal{N}=4$ holomorphic anomaly equations.
