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arXiv · 2111.01837

A skeletal model for 2d conformal AQFTs

Marco Benini·Luca Giorgetti·Alexander Schenkel
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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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Marco Benini, Luca Giorgetti, Alexander Schenkel. 2021-11-02. A skeletal model for 2d conformal AQFTs. https://doi.org/10.1007/s00220-022-04428-4

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