Quasi-Particles, Conformal Field Theory, and $q$-Series

TL;DR

This paper reviews how conformal field theory characters can be expressed as fermionic quasi-particle $q$-series, illustrating their construction with the integrable three-state Potts chain and connecting to Rogers-Ramanujan identities.

Contribution

It provides a detailed construction of fermionic representations of conformal characters for the three-state Potts model, linking CFT to $q$-series and Rogers-Ramanujan identities.

Findings

Fermionic $q$-series representations of CFT characters

Explicit construction for the three-state Potts chain

Connection to Rogers-Ramanujan identities

Abstract

We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain. These fermionic representations are $q$-series which are generalizations of the sums occurring in the Rogers-Ramanujan identities. (To appear in the proceedings of ``Yang-Baxter Equations in Paris'', July 1992, J.-M.~Maillard (ed.).)