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 supersymmetric level-one affine CFTs.
Fermionic CFTs from classical codes over finite fields
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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.
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Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
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 supersymmetric level-one affine CFTs.