Unitary and nonunitary A - D - E minimal models: coset graph fusion algebras, defects and dilogarithm identities
Paul A. Pearce, Jared J. Heymann, Thomas Quella
Abstract We consider unitary and nonunitary ( A , G ) coset minimal models on the cylinder with G = A , D , E . Elementary topological defects are implemented as non-contractible Verlinde, Pasquier and Ocneanu lines around the cylinder. The decomposition of compound defects, formed by fusing elementary defects together, is described by the Verlinde, Pasquier and Ocneanu graph fusion algebras. The action of the compound defects on the left- or right-vacuum boundary state builds the known conformal cylinder boundary conditions. Fusing these defects, in the presence of vacuum boundary conditions, reproduces the known general formulas for the conformal cylinder partition functions. We define the coset graph A ⊗ G / Z 2 , argue that it is a universal object and show that it encodes (i) the coset graph fusion algebra, (ii) the Affleck–Ludwig boundary g -factors, (iii) the defect g -factors given by quantum dimensions and (iv) the relative symmetry resolved Affleck–Ludwig entropies. Additionally, it is shown that the boundary and defect g -factors are related to the asymptotic counting of fusion paths on the coset graph. On the lattice, the defects are constructed as Yang–Baxter integrable seams including special braid and graph automorphism transfer matrices. Remarkably, many of the boundary conformal field theory (CFT) discrete structures, such as fusion matrices, modular matrices, quantum dimensions and defects, appear at the level of lattice Yang–Baxter integrable A - D - E restricted solid-on-solid models and these structures and their properties carry over to the CFT in the continuum scaling limit. Importantly, in the continuum scaling limit, the lattice transfer matrix T - and Y -system functional equations carry over to produce the coset graph fusion algebra for the defect lines. Moreover, 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.
arXiv:2512.21808•Journal of Physics A Mathematical and Theoretical•Sep 7, 2026•0 citations