Fermionic CFTs from classical codes over finite fields

Abstract

We construct a class of chiral fermionic CFTs from classical codes over finite fields whose order is a prime number. We exploit the relationship between classical codes and Euclidean lattices to provide the Neveu-Schwarz sector of fermionic CFTs. On the other hand, we construct the Ramond sector using the shadow theory of classical codes and Euclidean lattices. We give various examples of chiral fermionic CFTs through our construction. We also explore supersymmetric CFTs in terms of classical codes by requiring the resulting fermionic CFTs to satisfy some necessary conditions for supersymmetry.

arXiv comment52 pages, 4 figures; v2: typos corrected

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Cited by in corpus (8)

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• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Modular extension of topological orders from congruence representations
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Impact of conversion-driven processes on singlet-doublet Majorana dark matter relic
• Code CFTs and Topological Matter