The linear CS/WZW bulk/boundary system in AQFT

Abstract

This paper constructs in the framework of algebraic quantum field theory (AQFT) the linear Chern-Simons/Wess-Zumino-Witten system on a class of $3$-manifolds $M$ whose boundary $\partial M$ is endowed with a Lorentzian metric. It is proven that this AQFT is equivalent to a dimensionally reduced AQFT on a $2$-dimensional manifold $B$, whose restriction to the $1$-dimensional boundary $\partial B$ is weakly equivalent to a chiral free boson.

v2: 35 pages. Final version accepted for publication in Annales Henri Poincaré

References in corpus (4)

• Non-existence of natural states for Abelian Chern-Simons theory
• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• Strictification theorems for the homotopy time-slice axiom
• Spacetimes categories and disjointness for algebraic quantum field theory

Cited by in corpus (1)

• Green hyperbolic complexes on Lorentzian manifolds