Construction of modular branching functions from Bethe's equations in the 3-state Potts chain

We use the single-particle excitation energies and the completeness rules of the 3-state antiferromagnetic Potts chain, which have been obtained from Bethe's equation, to compute the modular invariant partition function. This provides a fermionic construction for the branching functions of theD₄ representation ofZ₄ parafermions which complements the bosonic constructions. It is found that there are oscillations in some of the correlations and a new connection with the field theory of the Lee-Yang edge is presented.