Fermionic Sum Representations for Conformal Field Theory Characters

TL;DR

This paper introduces fermionic sum representations for various conformal field theory characters, providing new mathematical tools and linking them to thermodynamic Bethe Ansatz, enhancing understanding of these models.

Contribution

It develops fermionic sum representations for a wide class of conformal field theory characters, extending previous bosonic formulations and connecting to thermodynamic Bethe Ansatz.

Findings

Fermionic sum representations for unitary Virasoro minimal models.

Extensions to non-unitary minimal models, coset theories, and superconformal series.

Connection of q→1 behavior to thermodynamic Bethe Ansatz.

Abstract

We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder construction. We also give fermionic representations for certain characters of the general $(G^{(1)})_k \times (G^{(1)})_l \over (G^{(1)})_{k+l}}$ coset conformal field theories, the non-unitary minimal models ${\cal M}(p,p+2)$ and ${\cal M}(p,kp+1)$, the $N$=2 superconformal series, and the $\ZZ_N$-parafermion theories, and relate the $q\to 1$ behaviour of all these fermionic sum representations to the thermodynamic Bethe Ansatz.