Coupled free fermion conformal field theories

Abstract

We study a specific class of CFTs that involve coupled free fermions, arising from parafermion CFTs and lattice constructions. We analyse their representation spaces and the underlying exclusion statistics of coupled free fermions using specific bases. In one particular case, we reveal an unexpected connection between the coset construction of parafermions, the lattice construction, and and orbifold thereof. This connection is supported by proving a range of character identities within the context of coupled free fermions. Simultaneously, we obtain explicit expressions of certain string functions in terms of Dedekind eta functions.