A skeletal model for 2d conformal AQFTs

Abstract

A simple model for the localization of the category ${\mathbf{CLoc}}_2$ of oriented and time-oriented globally hyperbolic conformal Lorentzian $2$-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of $2$-dimensional conformal algebraic quantum field theories (AQFTs) satisfying the time-slice axiom in terms of only two algebras, one for the $2$-dimensional Minkowski spacetime and one for the flat cylinder, together with a suitable action of two copies of the orientation preserving embeddings of oriented $1$-manifolds. The latter result is used to construct adjunctions between the categories of $2$-dimensional and chiral conformal AQFTs whose right adjoints formalize and generalize Rehren's chiral observables.

27 pages, final version accepted for publication in Communications in Mathematical Physics

References in corpus (1)

• Conformal generally covariant quantum field theory: The scalar field and its Wick products

Cited by in corpus (5)

• Wightman fields for two-dimensional conformal field theories with pointed representation category
• Strictification theorems for the homotopy time-slice axiom
• Homotopy theory of net representations
• Spacetimes categories and disjointness for algebraic quantum field theory
• Gluing algebraic quantum field theories on manifolds