# The linear CS/WZW bulk/boundary system in AQFT

February 14, 2023

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.

Keywords:

algebraic quantum field theory, boundary conditions in gauge theory, chiral conformal field theory, Chern-Simons theory, Wess-Zumino-Witten model