Conformal two-boundary loop model on the annulus

Abstract

We study the two-boundary extension of a loop model - corresponding to the dense phase of the O(n) model, or to the Q=n^2 state Potts model - in the critical regime -2 < n < 2. This model is defined on an annulus of aspect ratio τ. Loops touching the left, right, or both rims of the annulus are distinguished by arbitrary (real) weights which moreover depend on whether they wrap the periodic direction. Any value of these weights corresponds to a conformally invariant boundary condition. We obtain the exact seven-parameter partition function in the continuum limit, as a function of τ, by a combination of algebraic and field theoretical arguments. As a specific application we derive some new crossing formulae for percolation clusters.

34 pages, 10 figures

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• Associative-algebraic approach to logarithmic conformal field theories
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• The Jordan Structure of Two Dimensional Loop Models
• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model
• Jordan cells of periodic loop models
• Integrability and conformal data of the dimer model
• Discrete holomorphicity and integrability in loop models with open boundaries
• Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
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• Boundary transitions of the O(n) model on a dynamical lattice
• Conformal partition functions of critical percolation from $D_3$ Thermodynamic Bethe Ansatz equations
• Boundary changing operators in the O(n) matrix model
• $U_q{\mathfrak{sl}}_2$-invariant non-compact boundary conditions for the XXZ spin chain
• Edge states and conformal boundary conditions in super spin chains and super sigma models
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• Two-point boundary correlation functions of dense loop models
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• Logarithmic Minimal Models with Robin Boundary Conditions
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• Algebraic Bethe Ansatz for the Open XXZ Spin Chain with Non-Diagonal Boundary Terms via $U_{\mathfrak{q}}{\mathfrak{sl}}_2$ Symmetry
• Boundary critical phenomena in the quantum Ashkin-Teller model
• Boundary conformal field theories and loop models