Conformal boundary conditions in the critical \({\mathcal O}(n)\) model and dilute loop models. (English) Zbl 1203.81137
Summary: We study the conformal boundary conditions of the dilute \({\mathcal O}(n)\) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted in terms of symmetry breaking interactions in the \({\mathcal O}(n)\) model. We identify the corresponding boundary condition changing operators, Virasoro characters, and conformally invariant partition functions. We compute the entropies of the conformal boundary states, and organize the flows between the various boundary critical points in a consistent phase diagram. The operators responsible for the various flows are identified. Finally, we discuss the relation to open boundary conditions in the \({\mathcal O}(n)\) model, and present new crossing probabilities for Ising domain walls.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81R30 | Coherent states |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
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