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Narain CFTs and error-correcting codes on finite fields

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arxiv 2203.10848 v1 pith:COITBGKU submitted 2022-03-21 hep-th cs.ITmath.IT

classification hep-thcs.ITmath.IT
keywords cftscodesnarainspectralfiniteself-dualcalculatecapability
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abstract

We construct Narain CFTs from self-dual codes on the finite field $F_p$ through even self-dual lattices for any prime $p>2$. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error correction capability and the extended enumerator polynomial of the code. In particular, we calculate specific spectral gaps of CFTs constructed from codes and compare them with the largest spectral gap among all Narain CFTs.

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    Odd Lagrangian subgroups of the discriminant group of an abelian Chern-Simons theory give fermionic CFTs whose spectra are an NS lattice and its shadow, yielding new fermionic code CFTs and a classification of supersy...

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