标题： 从三维Gelca-Hamilton拓扑量子场论得到的二阶超弦纯量测度 显示英文标题

标题： Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT

摘要： 在超弦的路径积分表述中，沿着黎曼曲面的模变换，手征测度会获得一个相位。 这促使使用反常流入来通过一个模不变的$3$维理论的路径积分形式主义来定义超弦的手征测度。 A Gelca-Hamilton 拓扑场理论（TQFT）是 Atiyah 的一种在带有边界雅可比流形的$3$维扩展流形上的 TQFT，其希尔伯特空间由θ级数张成。 我们证明，在路径积分中，亏格$g\leq 2$的超弦手征测度可以通过在某些$3$维体扩展流形上的 Gelca-Hamilton TQFT 的路径积分得到。 超弦手征测度的模变换可以被理解为扩展映射类群在体$3$维扩展流形上的作用。 显示英文摘要

摘要： In the path integral formulation of the superstring, the chiral measure acquires a phase under the modular transformation of a Riemann surface. This motivated the use of anomaly inflow to define the superstring chiral measure by a path integral formalism of a modular invariant $3$-dimensional theory. A Gelca-Hamilton topological field theory (TQFT) is one of the Atiyah's TQFT on a $3$-dimensional extended manifold with the boundary Jacobi variety of a Riemann surface, whose Hilbert space is spanned by the theta series. We show that genus $g\leq 2$ superstring chiral measure in the path integral can be obtained by the path integral of the Gelca-Hamilton TQFT on some $3$-dimensional bulk extended manifolds. The modular transformation of the superstring chiral measure can be understood as the action of the extended mapping class group on the bulk $3$-dimensional extended manifolds.