Boundary Loop Models and 2D Quantum Gravity

Abstract

We study the O(n) loop model on a dynamically triangulated disk, with a new type of boundary conditions, discovered recently by Jacobsen and Saleur. The partition function of the model is that of a gas of self and mutually avoiding loops covering the disk. The Jacobsen-Saleur (JS) boundary condition prescribes that the loops that do not touch the boundary have fugacity n in [-2,2], while the loops touching at least once the boundary are given different fugacity y. The class of JS boundary conditions, labeled by the real number y, contains the Neumann (y=n) and Dirichlet (y=1) boundary conditions as particular cases. Here we consider the dense phase of the loop gas, where we compute the two-point boundary correlators of the L-leg operators with mixed Neumann-JS boundary condition. The result coincides with the boundary two-point function in Liouville theory, derived by Fateev, Zamolodchikov and Zamolodchikov. The Liouville charge of the boundary operators match, by the KPZ correspondence, with the L-leg boundary exponents conjectured by JS.

Typos corrected

References in corpus (10)

• D-branes in the WZW model
• Logarithmic Minimal Models
• Boundary Liouville Field Theory: Boundary Three Point Function
• Strings with Discrete Target Space
• Bulk-Boundary Propagator in Liouville Theory on a Disc
• Boundary Liouville Theory and 2D Quantum Gravity
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• Loop Gas Model for Open Strings
• Boundary Ground Ring in 2D String Theory
• Scattering of Open and Closed Strings in 1+1 Dimensions

Cited by in corpus (7)

• Critical Gaussian multiplicative chaos: Convergence of the derivative martingale
• Conformal boundary conditions in the critical O(n) model and dilute loop models
• Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
• 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 transitions of the O(n) model on a dynamical lattice
• Boundary changing operators in the O(n) matrix model