We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.

Belin, A., de Boer, J., Kruthoff, J. (2018). Comments on a state-operator correspondence for the torus. SCIPOST PHYSICS, 5(6) [10.21468/SciPostPhys.5.6.060].

Comments on a state-operator correspondence for the torus

Belin A;
2018

Abstract

We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.
Articolo in rivista - Articolo scientifico
AdS/CFT
English
Belin, A., de Boer, J., Kruthoff, J. (2018). Comments on a state-operator correspondence for the torus. SCIPOST PHYSICS, 5(6) [10.21468/SciPostPhys.5.6.060].
Belin, A; de Boer, J; Kruthoff, J
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/396370
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