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Comments on a state-operator correspondence for the torus

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      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.

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            Author and article information

            Affiliations
            [1 ]Institute of Physics, University of Amsterdam
            Journal
            SciPost Physics
            SciPost Phys.
            Stichting SciPost
            2018
            December 10 2018
            : 5
            : 6
            10.21468/SciPostPhys.5.6.060
            © 2018

            This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

            Physics

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