椭圆三联画
An Elliptic Triptych
摘要：
我们澄清了非紧椭圆亏格的三个方面。首先，从非线性σ模型描述出发，给出了雪茄共形场论椭圆亏格的路径积分推导。其结果是一个明显的模和在一个格。其次，我们讨论了具有连续谱的超对称量子力学。我们调整了理论并分析了由费米子数加权的迹线对温度的依赖性。这种依赖性是由监管机构决定的。从红外边界条件的依赖性的详细分析，我们认为，在非紧椭圆属右移超对称结合模协方差是反常的。第三，进一步阐明了平坦空间椭圆亏格与雪茄椭圆亏格的无限水平极限之间的关系。
英文摘要：
We clarify three aspects of non-compact elliptic genera. Firstly, we give a path integral derivation of the elliptic genus of the cigar conformal field theory from its non-linear sigma-model description. The result is a manifestly modular sum over a lattice. Secondly, we discuss supersymmetric quantum mechanics with a continuous spectrum. We regulate the theory and analyze the dependence on the temperature of the trace weighted by the fermion number. The dependence is dictated by the regulator. From a detailed analysis of the dependence on the infrared boundary conditions, we argue that in non-compact elliptic genera right-moving supersymmetry combined with modular covariance is anomalous. Thirdly, we further clarify the relation between the flat space elliptic genus and the infinite level limit of the cigar elliptic genus.
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