Boundary loop models coupled to 2D Quantum Gravity
Ivan Kostov
We give a matrix model description of the O(n) loop model with anisotropic boundary conditions.
The boundary two-point functions on the disk with ordinary/anisotropic boundary conditions
are expressed as one-trace matrix observables. We derive a loop equation for these correlators
and find its explicit solution in the scaling limit. The solution describes a perturbation of Liouville
gravity by the bulk and the boundary thermal operator (1,3)