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


Owen Gwilliam (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

Eugene Rabinovich (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)

Brian R. Williams (Department of Mathematics & Statistics, Boston University, Boston, Massachusetts, U.S.A.)


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.


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