Pure and Applied Mathematics Quarterly
Volume 18 (2022)
Special issue celebrating the work of Herb Clemens
Guest Editor: Ron Donagi
Factorization algebras and abelian CS/WZW-type correspondences
Pages: 1485 – 1553
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