发表机构
Ludwig–Maximilians–Universität München; Johannes Gutenberg-Universität（慕尼黑大学; 约翰内斯·古腾堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过四维N=1超对称规范理论的涡旋配分函数提出量子椭圆上同调概念，利用等变局域化计算U(1)理论，并探讨反常与Thom层及虚拟结构层的联系。
AI 中文摘要
在本文中，我们研究了四维N=1超对称规范理论在时空几何$T^2 \ imes D^2$上的非微扰涡旋配分函数，并提出这些配分函数提供了量子椭圆上同调的一种概念。对于特定的U(1)规范理论，我们通过将等变局域化方法应用于Handsaw箭图簇来显式计算这些配分函数，这些箭图簇为此特定类别的U(1)规范理论实现了非微扰涡旋扇区的模空间。所确定的涡旋配分函数被差分算子湮灭，这些算子被解释为N=(0,2)BPS曲面缺陷之间的Ward恒等式。与具有四个超电荷的低维规范理论相比，反常对于四维配分函数的一致表述起着至关重要的作用。在我们提出的用等变椭圆上同调对涡旋配分函数进行数学表述的方案中，规范理论反常与对应于相关拟映射模空间的Thom层的几何性质相关。受显式计算的启发，我们反思了在一般量子椭圆上同调数学理论中，拟映射模空间上是否存在‘虚拟结构层’。
英文摘要
In this paper, we study non-perturbative vortex partition functions of four-dimensional N=1 supersymmetric gauge theories on the space-time geometry $T^2 \times D^2$, and we propose that these partition functions offer a notion of quantum elliptic cohomology. For particular U(1)-gauge theories we calculate these partition functions explicitly by applying equivariant localization methods to Handsaw quiver varieties that realize for this particular class of U(1)-gauge theories the moduli spaces of the non-perturbative vortex sectors. The determined vortex partition functions are annihilated by difference operators, which are interpreted as Ward identities among N=(0,2) BPS surface defects. Compared to lower dimensional gauge theories with four supercharges, anomalies play an essential role for a consistent formulation of the four-dimensional partition functions. In our proposal towards a mathematical formulation of the vortex partition functions in terms of equivariant elliptic cohomology, the gauge theory anomalies relate to geometric properties of the Thom sheaves corresponding to the relevant quasimap moduli spaces. Motivated by the explicit computations we reflect on the existence of a `virtual structure sheaf' on the moduli space of quasimaps for a general mathematical theory of quantum elliptic cohomology.
Comments72 pages
