Liouville quantum gravity — holography, JT and matrices

A bstract We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. find explicit formulas describing the gravitational dressing of bulk boundary correlators in disk. Their structure has a striking resemblance observables 2d BF (plus term), associated to quantum deformation SL (2 , ?), connection we develop some detail. For case p ) theory, compare match results from continuum approach matrix model calculation, verify that large limit Jackiw-Teitelboim gravity. consider multi-boundary amplitudes write terms gluing one-point functions using Weil-Petersson volumes measures. Generating for genus zero are derived, taking limit. Finally, present preliminary evidence can be interpreted as dilaton sinh ? potential.