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)

http://scgp.stonybrook.edu/video_portal/video.php?id=2437

Simons- Perspectives, Open Problems & Applications of Quantum Liouville Theory