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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.
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Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor N of an RCFT and the quadratic residues modulo N play an important role in the computation and classification of Galois permutations. We establish a field correspondence in different theories through the picture of effective central charge, which combines Galois inner automorphisms and the structure of simple currents. We then make a first attempt to extend Hecke operators to the full data of modular tensor categories. The Galois symmetry encountered in the modular data transforms the fusion and the braiding matrices as well, and yields isomorphic structures in theories related by Hecke operators.
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- Award ID(s):
- 1818875
- PAR ID:
- 10299125
- Date Published:
- Journal Name:
- Journal of physics
- Volume:
- 53
- Issue:
- 33
- ISSN:
- 0368-3400
- Page Range / eLocation ID:
- 334003
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1751-8121/ab8e03
