Permutation orbifolds and holography
Permutation orbifolds and holography
Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold technology. In particular, we describe the group theoretic constraints on permutation groups to ensure a (stringy) holographic CFT. The primary result we uncover is that in order for the degeneracy of states to be finite in the large central charge limit, the groups of interest are the so-called oligomorphic permutation groups. Further requiring that the low-lying spectrum be sparse enough puts a bound on the number of orbits of these groups (on finite element subsets). Along the way we also study familiar cyclic and symmetric orbifolds to build intuition. We also demonstrate how holographic spectral properties are tied to the geometry of covering spaces for permutation orbifolds.
hep-th, gr-qc
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
30 March 2015
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
Haehl, Felix M. and Rangamani, Mukund
(2015)
Permutation orbifolds and holography.
JHEP, 2015 (3), [163].
(doi:10.1007/JHEP03(2015)163).
Abstract
Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold technology. In particular, we describe the group theoretic constraints on permutation groups to ensure a (stringy) holographic CFT. The primary result we uncover is that in order for the degeneracy of states to be finite in the large central charge limit, the groups of interest are the so-called oligomorphic permutation groups. Further requiring that the low-lying spectrum be sparse enough puts a bound on the number of orbits of these groups (on finite element subsets). Along the way we also study familiar cyclic and symmetric orbifolds to build intuition. We also demonstrate how holographic spectral properties are tied to the geometry of covering spaces for permutation orbifolds.
More information
Accepted/In Press date: 9 March 2015
Published date: 30 March 2015
Additional Information:
47 pages, 4 figures. v2: added comments. v3: minor improvements, published version
Keywords:
hep-th, gr-qc
Identifiers
Local EPrints ID: 471227
URI: http://eprints.soton.ac.uk/id/eprint/471227
ISSN: 1126-6708
PURE UUID: 21a8fcdd-ee4c-45b8-89b9-968a1d7d66c1
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Date deposited: 01 Nov 2022 17:32
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Felix M. Haehl
Author:
Mukund Rangamani
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