扭曲母线的高阶极点和交叉现象
Higher Poles and Crossing Phenomena from Twisted Genera
摘要：
我们证明了具有高阶极点的Appell-Lerch和以及它们的模协变完备化作为配分函数出现在具有世界片超对称性的雪茄共形场论中.雪茄的椭圆属的模协变导数产生对应于右移动量、左移费米子数的（幂）算子插入，以及对应于普通零模分区和的项。为了证明这一点，我们证明了右移超对称量子力学（特别是哈密顿量和谱密度）如何依赖于角动量的化学势的虚部。作为我们的分析的结果，我们发现，改变雪茄的角动量的化学势的虚部引起的边界状态的贡献的椭圆属的跨壁现象，而完整的椭圆属是一个连续的函数的化学势。
英文摘要：
We demonstrate that Appell-Lerch sums with higher order poles as well as their modular covariant completions arise as partition functions in the cigar conformal field theory with worldsheet supersymmetry. The modular covariant derivatives of the elliptic genus of the cigar give rise to operator insertions corresponding to (powers of) right-moving momentum, left-moving fermion number, as well as a term corresponding to an ordinary zero mode partition sum. To show this, we demonstrate how the right-moving supersymmetric quantum mechanics (and in particular the Hamiltonian and spectral density) depend on the imaginary part of the chemical potential for angular momentum. As a consequence of our analysis we find that varying the imaginary part of the chemical potential for angular momentum on the cigar gives rise to a wall-crossing phenomenon in the bound state contribution to the elliptic genus, while the full elliptic genus is a continuous function of the chemical potential.
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