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.

arXiv commentv2: 35 pages. Final version accepted for publication in Annales Henri Poincaré

References in corpus (15)

• The generally covariant locality principle -- A new paradigm for local quantum physics
• Perturbative quantum gauge theories on manifolds with boundary
• Classical BV theories on manifolds with boundary
• Homotopy theory of algebraic quantum field theories
• Operads for algebraic quantum field theory
• Algebraic quantum field theory on spacetimes with timelike boundary
• Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary
• Towards holography in the BV-BFV setting
• Linear Yang-Mills theory as a homotopy AQFT
• Higher Structures in Algebraic Quantum Field Theory
• 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
• On Maxwell's Equations on Globally Hyperbolic Spacetimes with Timelike Boundary
• Spacetimes categories and disjointness for algebraic quantum field theory

Cited by in corpus (1)

• Green hyperbolic complexes on Lorentzian manifolds