Unitary and Nonunitary A-D-E minimal models: Coset graph fusion algebras, defects, entropies, SREEs and dilogarithm identities

TL;DR

This paper explores the algebraic and lattice structures of A-D-E minimal models with topological defects, revealing new connections between fusion algebras, boundary entropies, and dilogarithm identities in conformal field theory.

Contribution

It introduces a coset graph framework that encodes fusion, boundary, defect, and entanglement properties, linking lattice models with conformal field theory structures.

Findings

Fusion algebra and boundary g-factors are encoded in the coset graph.

Defects are implemented via special face weights in lattice models.

Effective central charges are expressed through dilogarithms of quantum dimensions.

Abstract

We consider both unitary and nonunitary A-D-E minimal models on the cylinder with topological defects along the non-contractible cycle of the cylinder. We define the coset graph $A \otimes G/\mathbb{Z}_2$ and argue that it encodes not only the (i) coset graph fusion algebra, but also (ii) the Affleck-Ludwig boundary g-factors; (iii) the defect g-factors (quantum dimensions) and (iv) the relative symmetry resolved entanglement entropy. By studying A-D-E restricted solid-on-solid models, we find that these boundary conformal field theory structures are also present on the lattice: defects (seams) are implemented by face weights with special values of the spectral parameter. Integrability allows the study of lattice transfer matrix T- and Y-system functional equations to reproduce the fusion algebra of defect lines. The effective central charges and conformal weights are expressed in terms of dilogarithms of the braid and bulk asymptotics of the Y-system expressed in terms of the quantum dimensions.