论文标题
Chern字符的超对称场理论
Chern characters for supersymmetric field theories
论文作者
论文摘要
当$ d = 1 $和复杂的分析椭圆形的共同体时，我们从$ d | 1 $ d | 1 $ dimensional euclidean fieldean Field Theories构建地图。这为Stolz- Teichner计划提供了进一步的证据，同时还可以在其框架内识别Chern角色的候选几何模型。该结构是作为Fei Han对K理论中Chern特征实现的更高维度和参数化的概括而产生的，作为尺寸减少$ 1 | 1 $维欧几里得田地理论。在椭圆形的情况下，主要的新功能是超级模量空间的几何形状$ 2 | 1 $二维的Tori与复杂的分析椭圆共同体的几何形状之间的微妙相互作用。作为推论，我们获得了一个完全的几何证据，即$ \ MATHCAL {n} =（0,1）$ supersymmetric量子场理论的分区函数是在Stolz和Teichner的建议之后，是弱模块化形式。
We construct a map from $d|1$-dimensional Euclidean field theories to complexified K-theory when $d=1$ and complex analytic elliptic cohomology when $d=2$. This provides further evidence for the Stolz--Teichner program, while also identifying candidate geometric models for Chern characters within their framework. The construction arises as a higher-dimensional and parameterized generalization of Fei Han's realization of the Chern character in K-theory as dimensional reduction for $1|1$-dimensional Euclidean field theories. In the elliptic case, the main new feature is a subtle interplay between the geometry of the super moduli space of $2|1$-dimensional tori and the derived geometry of complex analytic elliptic cohomology. As a corollary, we obtain an entirely geometric proof that partition functions of $\mathcal{N}=(0,1)$ supersymmetric quantum field theories are weak modular forms, following a suggestion of Stolz and Teichner.
