A Skeletal Model for 2d Conformal AQFTs

Benini, Marco; Giorgetti, Luca; Schenkel, Alexander

Abstract

A simple model for the localization of the category CLoc2 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.

Citation

Benini, M., Giorgetti, L., & Schenkel, A. (2022). A Skeletal Model for 2d Conformal AQFTs. Communications in Mathematical Physics, 395(1), 269-298. https://doi.org/10.1007/s00220-022-04428-4

• Journal Article Type: Article
• Acceptance Date: May 19, 2022
• Online Publication Date: Aug 14, 2022
• Publication Date: 2022-10
• Deposit Date: Aug 3, 2022
• Publicly Available Date: Aug 14, 2022
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 395
• Issue: 1
• Pages: 269-298
• DOI: https://doi.org/10.1007/s00220-022-04428-4
• Keywords: Mathematical Physics; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/9583742
• Publisher URL: https://link.springer.com/article/10.1007/s00220-022-04428-4