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Title: Holographic description of Narain CFTs and their code-based ensembles
A<sc>bstract</sc> We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central chargec=n, and a sum of (U(1) × U(1))nChern-Simons theories on different handlebody topologies. We begin by reviewing the general relation of additive codes to Narain CFTs. Then we describe a holographic duality between any given Narain theory and a pure Chern-Simons theory on a handlebody manifold. We proceed to consider an ensemble of Narain theories, defined in terms of an ensemble of codes of lengthnoverℤk × ℤkfor primek. We show that averaging over this ensemble is holographically dual to a level-k(U(1) × U(1))nChern-Simons theory, summed over a finite number of inequivalent classes of handlebody topologies. In the limit of largekthe ensemble approaches the ensemble of all Narain theories, and its bulk dual becomes equivalent to “U(1)-gravity” — the sum of the pertubative part of the Chern-Simons wavefunction over all possible handlebodies — providing a bulk microscopic definition for this theory. Finally, we reformulate the sum over handlebodies in terms of Hecke operators, paving the way for generalizations.  more » « less
Award ID(s):
2310426
PAR ID:
10521426
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer (Journal of High Energy Physics)
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2024
Issue:
5
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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