A skeletal model for 2d conformal AQFTs

TL;DR

This paper introduces a simplified model for 2D conformal algebraic quantum field theories, describing them via two core algebras and actions, and establishes categorical adjunctions linking 2D and chiral theories.

Contribution

It constructs a skeletal model for 2D conformal AQFTs, reducing their description to two algebras and actions, and develops adjunctions to connect 2D and chiral conformal theories.

Findings

Provides an equivalent description of 2D conformal AQFTs with two algebras.

Constructs adjunctions between 2D and chiral conformal AQFT categories.

Generalizes Rehren's chiral observables through categorical frameworks.

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.