论文标题
超对称分区功能的模块化
Modularity of supersymmetric partition functions
论文作者
论文摘要
我们发现了具有四个维度的R-对称性的超对称理论的超对称分区功能的模块化特性。从某种意义上说，这种模块化特性是二维超对称理论在圆环（即椭圆属）上的超对称分区函数的模块化不变性的概括。所讨论的分区功能是在通过粘合固体托里获得的歧管同构的。这种胶合涉及选择边界圆环的大型差异性，以及为背景风味对称性连接（如果存在）的大型量规变换。我们的模块化属性是胶合过程一致性的表现。模块化特性用于重新层次的超对称性钟形公式，用于四维规格理论，在计算超对称黑洞的熵中起着关键作用。要具体，我们使用四维n = 1个超对称理论，但我们希望结果的版本将更广泛地应用于其他维度的超对称理论。
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric partition function of two-dimensional supersymmetric theories on a torus i.e. of the elliptic genus. The partition functions in question are on manifolds homeomorphic to the ones obtained by gluing solid tori. Such gluing involves the choice of a large diffeomorphism of the boundary torus, along with the choice of a large gauge transformation for the background flavor symmetry connections, if present. Our modular property is a manifestation of the consistency of the gluing procedure. The modular property is used to rederive a supersymmetric Cardy formula for four-dimensional gauge theories that has played a key role in computing the entropy of supersymmetric black holes. To be concrete, we work with four-dimensional N=1 supersymmetric theories but we expect versions of our result to apply more widely to supersymmetric theories in other dimensions.
