Fermionic CFTs from classical codes over finite fields
Kohki Kawabata, Shinichiro Yahagi
Abstract
A bstract 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.
Topics & Concepts
PhysicsEuclidean geometrySupersymmetryTheoretical physicsMathematical physicsClass (philosophy)Order (exchange)Conformal mapPrime (order theory)CombinatoricsMathematicsGeometryFinanceArtificial intelligenceEconomicsComputer scienceAlgebraic structures and combinatorial modelsCoding theory and cryptographyFinite Group Theory Research