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This paper addresses the following question: given a topological quantumfield theory on $\mathbb R^n$ built from an action functional, when is itpossible to globalize the theory so that it makes sense on an arbitrary smoothoriented $n$-manifold? We study a broad class of topological field theories --those of AKSZ type -- and obtain an explicit condition for the vanishing of theframing anomaly, i.e., the obstruction to performing this globalizationprocedure. We also interpret our results in terms of identifying theobservables as an algebra over the framed little $n$-disks operad. Our analysisuses the BV formalism for perturbative field theory and the notion offactorization homology.

Framed $\mathbb E_n$-Algebras from Quantum Field Theory