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.

Benini, M., Giorgetti, L., Schenkel, A. (2022). A skeletal model for 2d conformal AQFTs. COMMUNICATIONS IN MATHEMATICAL PHYSICS [10.1007/s00220-022-04428-4].

### 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.
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Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05
English
Mathematical Physics
Mathematical Physics
High Energy Physics - Theory
Mathematics - Category Theory
Mathematics - Mathematical Physics
81Txx, 53C50
http://arxiv.org/abs/2111.01837v2
Benini, M., Giorgetti, L., Schenkel, A. (2022). A skeletal model for 2d conformal AQFTs. COMMUNICATIONS IN MATHEMATICAL PHYSICS [10.1007/s00220-022-04428-4].
Benini, M; Giorgetti, L; Schenkel, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/303688
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