Local State Probabilities of Solvable Lattice Models: Relatives of $A_{n}^{(1)}$ Family

TL;DR

This paper investigates local state probabilities in solvable lattice models related to rational conformal field theories, providing exact results and conjectures for higher rank models based on $A_{n}^{(1)}$ family structures.

Contribution

It offers explicit calculations of local state probabilities for models connected to $SO(3)_{4 R}$ WZW theories and proposes conjectures for higher rank relatives of $A_{n}^{(1)}$ face models.

Findings

Explicit LSP results for models based on $SO(3)_{4 R}$ WZW theory.

Conjectures for LSP in higher rank $A_{n}^{(1)}$ face models.

Insights into the structure of solvable lattice models related to conformal field theories.

Abstract

We present the results for the local state probabilities (LSP) of the solvable lattice models, constructed around rational conformal field theory given by WZW model on $SO(3)_{4 R}=SU(2)_{4 R} / Z_{2}$ together with primary field $\phi_{1}$(symmetric tensor of degree 2). Some conjectures for the LSP for some higher rank relatives of $A_{n}^{(1)}$ face models are also presented.