论文标题
分数化同源性和数学物理学应用中的应用i：基础
Equivariant localization in factorization homology and applications in mathematical physics I: Foundations
论文作者
论文摘要
我们开发了一种与弗朗西斯 - 基准竞争者[fg]和贝林森 - 德林菲尔德[bd1]的定义，以相互连接的代数$ g $的作用在品种上建立了对等值的代数。 We define an equivariant analogue of factorization homology, valued in modules over $\text{H}^\bullet_G(\text{pt})$, and in the case $G=(\mathbb{C}^\times)^n$ we prove an equivariant localization theorem for factorization homology, analogous to the classical localization theorem [AtB].我们建立了$ \ Mathbb {C}^\ times $ epivariant分解代数之间的关系，并过滤了其对固定点亚变量的限制。这些结果为[NEK1]中引入的$ω$ background构造的物理文献的预测提供了模型，解释了分解$ \ MATHBB {E} _n $代数作为混合溶性量子量子量子理论中的可观察力。 在同伴论文[BU2]中，我们开发了工具来提供分解的几何结构$ \ mathbb {e} _n $代数，并将它们应用它们定义与低维度中超对称性理论相对应的那些相对应的那些。此外，我们将上述结果应用于这些示例，以说明[COSG]和[BEEM4]的预测，并从这个角度解释这些结构之间的关系。
We develop a theory of equivariant factorization algebras on varieties with an action of a connected algebraic group $G$, extending the definitions of Francis-Gaitsgory [FG] and Beilinson-Drinfeld [BD1] to the equivariant setting. We define an equivariant analogue of factorization homology, valued in modules over $\text{H}^\bullet_G(\text{pt})$, and in the case $G=(\mathbb{C}^\times)^n$ we prove an equivariant localization theorem for factorization homology, analogous to the classical localization theorem [AtB]. We establish a relationship between $\mathbb{C}^\times$ equivariant factorization algebras and filtered quantizations of their restrictions to the fixed point subvariety. These results provide a model for predictions from the physics literature about the $Ω$-background construction introduced in [Nek1], interpreting factorization $\mathbb{E}_n$ algebras as observables in mixed holomorphic-topological quantum field theories. In the companion paper [Bu2], we develop tools to give geometric constructions of factorization $\mathbb{E}_n$ algebras, and apply them to define those corresponding to holomorphic-topological twists of supersymmetric gauge theories in low dimensions. Further, we apply our above results in these examples to give an account of the predictions of [CosG] as well as [Beem4], and explain the relation between these constructions from this perspective.
