Narain CFTs and error-correcting codes on finite fields

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.

arXiv comment19 pages, 1 figure

References in corpus (13)

• Target Space Duality in String Theory
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Notes on the K3 Surface and the Mathieu group M_24
• Free partition functions and an averaged holographic duality
• Constraints on 2d CFT partition functions
• Holographic tensor network models and quantum error correction: A topical review
• Conformal Field Theories, Representations and Lattice Constructions
• Sphere Packing and Quantum Gravity
• Comments on the holographic description of Narain theories
• High-dimensional sphere packing and the modular bootstrap
• Non-rational Narain CFTs from codes over $F_4$
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• Classical Codes and Chiral CFTs at Higher Genus

Cited by in corpus (11)

• Fermionic CFTs from classical codes over finite fields
• Narain CFTs and Quantum Codes at Higher Genus
• Holographic description of Narain CFTs and their code-based ensembles
• Relation between spectra of Narain CFTs and properties of associated boolean functions
• Fake Z
• TQFT gravity and ensemble holography
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Optimal Narain CFTs from Codes
• Code CFTs and Topological Matter
• Algebraic constructions of code lattices in Narain conformal field theories