Homotopy transfer for QFT on non-compact manifold with boundary: a case study

Abstract

In this work we report a homological perturbation calculation to construct effective theories of topological quantum mechanics on R 0 . Such calculation can be regarded as a generalization of Feynman graph computation. The resulting effective theories fit into derived BV algebra structure, which generalizes BV quantization. Besides, our construction may serve as the simplest example of a process called "boundary transfer", which may help study bulk-boundary correspondence.

Perturbative BV-BFV formalism with homotopic renormalization: a case study

“…In Section 5, we extract the BV description of TQM in [WY22] from the BV-BFV description in Section 3 and Section 4. Then, mQME is reinterpreted from the perspective of factorization algebra developed in [CG16,CG21].…”

“…We could use it to define the theory still within BV formalism (which is the method in [WY22]). However, the spirit of BV-BFV formalism is that, we should work on E instead of the subspace E L ⊂ E only.…”

“…which is the field space we have studied in [WY22]. By constructions in [Rab21], we have a family of differential BV structures on O(E L ), concluded in [WY22, Proposition 3.0.2].…”

“…In [WY22] we only work on the restricted bulk field space E L , and define the theory within BV formalism. This approach is taken in several other works to deal with QFT's on manifold with boundary, such as [Rab21, GRW20, GW19, Zen21].…”