Hidden E type structures in dilute A models

TL;DR

This paper investigates the hidden E7 and E6 algebraic structures in dilute A models, connecting lattice models with conformal field theory through thermodynamic analysis and functional relations.

Contribution

It demonstrates the emergence of universal Y-systems and TBA equations for E6 and E7 from dilute A models, linking lattice models to algebraic structures in CFT.

Findings

Recovered Y-systems for E6 and E7 from dilute A models

Established connection between lattice models and algebraic structures in CFT

Analyzed thermodynamics via quantum transfer matrix approach

Abstract

The hidden E_{7} (E_{6}) structure has been conjectured for the minimal model ${\cal M}_{4,5} ({\cal M}_{6,7}$) perturbed by $\Phi_{1,2}$ in the context of conformal field theory(CFT). Motivated by this, we examine the dilute A_{4, 6} models, which are expected to be corresponding lattice models. Thermodynamics of the equivalent one dimensional quantum systems is analyzed via the quantum transfer matrix approach. Appropriate auxiliary functions, related to kinks in the theory, play a role in constructing functional relations among transfer matrices. We successfully recover the universal Y- systems and thereby Thermodynamic Bethe Ansatz equations for E_{6,7} from the dilute A_{6,4} model, respectively.