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- W4387560647 abstract "We provide a precise relation between an ensemble of Narain conformal field theories (CFTs) with central charge $c=n$, and a sum of $(U(1) times U(1))^n$ Chern-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 length $n$ over ${mathbb Z}_k times {mathbb Z}_k$ for prime $k$. We show that averaging over this ensemble is holographically dual to a level-$k$ $(U(1) times U(1))^n$ Chern-Simons theory, summed over a finite number of inequivalent classes of handlebody topologies. In the limit of large $k$ the 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." @default.
- W4387560647 created "2023-10-12" @default.
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- W4387560647 date "2023-10-09" @default.
- W4387560647 modified "2023-10-13" @default.
- W4387560647 title "Holographic description of Narain CFTs and their code-based ensembles" @default.
- W4387560647 doi "https://doi.org/10.48550/arxiv.2310.06012" @default.
- W4387560647 hasPublicationYear "2023" @default.
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