Fermionic CFTs from topological boundaries in abelian Chern-Simons theories

TL;DR

This paper constructs fermionic conformal field theories from bosonic abelian Chern-Simons theories by imposing topological boundary conditions, revealing new fermionic symmetries and classifications relevant to supersymmetric models.

Contribution

It introduces a method to derive fermionic CFTs from bosonic topological theories, including fermionic generalizations of code CFTs and classifications of boundary conditions for supersymmetric cases.

Findings

Fermionic CFTs can be obtained from bosonic abelian Chern-Simons theories.

The approach yields fermionic CFTs with affine Lie algebra symmetries.

Classification of boundary conditions leads to supersymmetric fermionic CFTs.

Abstract

A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that emerge from bosonic abelian Chern-Simons theories, playing the role of a symmetry topological field theory, by imposing topological boundary conditions. Our construction includes the fermionic generalization of code CFTs. When the Chern-Simons theory is associated with the root lattice of a simply laced Lie algebra, this approach yields a fermionic CFT with a level-one affine Lie algebra symmetry. As an application, we consider the Chern-Simons theories corresponding to a class of supersymmetric vertex operator algebras studied by Johnson-Freyd and classify their fermionic topological boundary conditions that give rise to supersymmetric CFTs.