The linear CS/WZW bulk/boundary system in AQFT

TL;DR

This paper constructs a linear Chern-Simons/Wess-Zumino-Witten system within algebraic quantum field theory on 3-manifolds with Lorentzian boundary, showing its equivalence to a reduced 2D AQFT with boundary chiral bosons.

Contribution

It introduces a new AQFT model for the CS/WZW system on 3-manifolds with Lorentzian boundary and demonstrates its dimensional reduction and boundary behavior.

Findings

AQFT model for CS/WZW system on 3-manifolds

Dimensional reduction to 2D AQFT

Boundary restriction to chiral free boson

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.