This paper addresses the following question: given a topological quantum field theory on ${ℝ}^n$ built from an action functional, when is it possible to globalize the theory so that it makes sense on an arbitrary smooth oriented n-manifold? We study a broad class of topological field theories — those of AKSZ type — and obtain an explicit condition for the vanishing of the framing anomaly, i.e. the obstruction to performing this globalization procedure. We also interpret our results in terms of identifying the observables as an algebra over the framed little n-disks operad. Our analysis uses the BV formalism for perturbative field theory and the notion of factorization homology.

本文解决了以下问题：给定拓扑量子场论${ℝ}^n$从动作泛函构建而来，什么时候可以全球化该理论，使其在任意平滑导向的n流形上有意义？我们研究了一大类拓扑场论（AKSZ 类型的拓扑场论），并获得了框架异常消失的明确条件，即执行全球化过程的障碍。我们还通过将可观测量识别为框架小n盘操作上的代数来解释我们的结果。我们的分析使用微扰场论的 BV 形式和因式分解同调的概念。