SOLUTION OF FUNCTIONAL EQUATIONS OF RESTRICTED $A_{n-1}^{(1)}$ FUSED LATTICE MODELS

TL;DR

This paper analytically solves functional fusion hierarchy equations for transfer matrices in restricted $A_{n-1}^{(1)}$ lattice models, revealing finite-size spectra, central charges, and conformal weights linked to coset conformal field theories.

Contribution

It provides an analytical solution to fusion hierarchy equations for these models, connecting lattice results with conformal field theory via Rogers dilogarithm.

Findings

Finite-size scaling spectra determined

Central charges computed explicitly

Conformal weights identified for coset theories

Abstract

Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted $A_{n-1}^{(1)}$ lattice models of Jimbo, Miwa and Okado. Specifically, these equations are solved analytically for the finite-size scaling spectra, central charges and some conformal weights. The results are obtained in terms of Rogers dilogarithm and correspond to coset conformal field theories based on the affine Lie algebra $A_{n-1}^{(1)}$ with GKO pair $A^{(1)}_{n-1}\; \oplus A^{(1)}_{n-1}\;\supset \; A^{(1)}_{n-1}$.