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# Pure and Applied Mathematics Quarterly

## Volume 18 (2022)

### Number 4

### Special issue celebrating the work of Herb Clemens

Guest Editor: Ron Donagi

### Factorization algebras and abelian CS/WZW-type correspondences

Pages: 1485 – 1553

DOI: https://dx.doi.org/10.4310/PAMQ.2022.v18.n4.a7

#### Authors

#### Abstract

We develop a method of quantization for free field theories on manifolds with boundary where the bulk theory is topological in the direction normal to the boundary and a local boundary condition is imposed. Our approach is within the Batalin–Vilkovisky formalism. At the level of observables, the construction produces a stratified factorization algebra that in the bulk recovers the factorization algebra introduced by Costello and Gwilliam. The factorization algebra on the boundary stratum enjoys a perturbative bulk-boundary correspondence with this bulk factorization algebra. A central example is the factorization algebra version of the abelian Chern–Simons/Wess–Zumino–Witten correspondence, but we examine higher dimensional generalizations that are related to holomorphic truncations of string theory andM-theory and involve intermediate Jacobians.

#### Keywords

factorization algebras, Chern–Simons theory, Wess–Zumino–Witten theory, bulk-boundary correspondence, Batalin–Vilkovisky formalism

#### 2010 Mathematics Subject Classification

Primary 81T20. Secondary 18G10, 58D29, 81T70.

Received 24 February 2021

Received revised 29 June 2021

Accepted 13 July 2021

Published 25 October 2022