Integrable Boundaries, Conformal Boundary Conditions and A-D-E Fusion Rules

Abstract

The $sl(2)$ minimal theories are labelled by a Lie algebra pair $(A,G)$ where $G$ is of $A$-$D$-$E$ type. For these theories on a cylinder we conjecture a complete set of conformal boundary conditions labelled by the nodes of the tensor product graph $A\otimes G$. The cylinder partition functions are given by fusion rules arising from the graph fusion algebra of $A\otimes G$. We further conjecture that, for each conformal boundary condition, an integrable boundary condition exists as a solution of the boundary Yang-Baxter equation for the associated lattice model. The theory is illustrated using the $(A_4,D_4)$ or 3-state Potts model.

4 pages, REVTeX

References in corpus (3)

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• On the Classification of Bulk and Boundary Conformal Field Theories
• Completeness of boundary conditions for the critical three-state Potts model

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