Supersymmetric Analogs of the Gordon-Andrews Identities, and Related TBA Systems

TL;DR

This paper extends classical q-series identities to supersymmetric models, providing new fermionic forms for characters of N=1 superconformal theories and linking them to TBA systems and representation theory.

Contribution

It introduces novel fermionic character formulas for SM(2,4k) models and connects these to two families of TBA systems, expanding the understanding of supersymmetric conformal field theories.

Findings

Derived two fermionic forms for SM(2,4k) characters.

Linked these forms to two TBA system families.

Discussed implications for q-series identities and representation theory.

Abstract

The Gordon-Andrews identities, which generalize the Rogers-Ramanujan-Schur identities, provide product and fermionic forms for the characters of the minimal conformal field theories (CFTs) M(2,2k+1). We discuss/conjecture identities of a similar type, providing two different fermionic forms for the characters of the models SM(2,4k) in the minimal series of N=1 super-CFTs. These two forms are related to two families of thermodynamic Bethe Ansatz (TBA) systems, which are argued to be associated with the $\hat{\phi}_{1,3}^{\rm top}$- and $\hat{\phi}_{1,5}^{\rm bot}$-perturbations of the models SM(2,4k). Certain other q-series identities and TBA systems are also discussed, as well as a possible representation-theoretical consequence of our results, based on Andrews's generalization of the Gollnitz-Gordon theorem.