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.
Orbifolds of chiral fermionic CFTs and their duality
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abstract
We consider chiral fermionic conformal field theories (CFTs) constructed from lattices and investigate their orbifolds under reflection and shift $\mathbb{Z}_2$ symmetries. For lattices based on binary error-correcting codes, we show the duality between reflection and shift orbifolds using a triality structure inherited from the binary codes. Additionally, we systematically compute the partition functions of the orbifold theories for both binary and nonbinary codes. Finally, we explore applications of this code-based construction in the search for supersymmetric CFTs and chiral fermionic CFTs without continuous symmetries.
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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.