Conformal boundary conditions in the critical O(n) model and dilute loop models

Abstract

We study the conformal boundary conditions of the dilute 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 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 O(n) model, and present new crossing probabilities for Ising domain walls.

49 pages, 21 figures

References in corpus (12)

• 2D growth processes: SLE and Loewner chains
• Associative-algebraic approach to logarithmic conformal field theories
• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• Conformal boundary loop models
• Discretely Holomorphic Parafermions and Integrable Loop Models
• The two-boundary Temperley-Lieb algebra
• Topological order from quantum loops and nets
• The O(n) model on the annulus
• Exact solution of the anisotropic special transition in the O(n) model in 2D
• Boundary operators in the O(n) and RSOS matrix models
• Boundary Loop Models and 2D Quantum Gravity
• Boundary changing operators in the O(n) matrix model

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• Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
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• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• The ghost algebra and the dilute ghost algebra
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• Geometric Exponents of Dilute Logarithmic Minimal Models