Comments on a state-operator correspondence for the torus
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 associa...
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| Format: | Article |
| Language: | English |
| Published: |
SciPost
2018-12-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.5.6.060 |
| Summary: | 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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| ISSN: | 2542-4653 |