Abstract
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of SL(2, ℝ), a connection we develop in some detail. For the case of the (2, p) minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large p limit the correlators match with Jackiw-Teitelboim gravity. We consider multi-boundary amplitudes that we write in terms of gluing bulk one-point functions using a quantum deformation of the Weil-Petersson volumes and gluing measures. Generating functions for genus zero Weil-Petersson volumes are derived, taking the large p limit. Finally, we present preliminary evidence that the bulk theory can be interpreted as a 2d dilaton gravity model with a sinh Φ dilaton potential.
Highlights
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries
The latter can be viewed as a double-scaled matrix integral [25] that in the continuum description becomes a non-critical string theory described by Liouville CFT, coupled to a minimal model and the bc ghost sector
Since there is a substantial amount of evidence in favor of a random matrix description of these models, finding JT gravity within a limiting situation illustrates that it is in hindsight not a surprise at all that JT gravity is a matrix integral
Summary
One of the most exciting developments the past few years, is the discovery of exactly solvable models of quantum gravity, starting with Kitaev’s SYK models [1], going through bulk Jackiw-Teitelboim (JT) gravity [5, 7] and its correlation functions [11,12,13,14,15,16,17, 19], and leading to the inclusion of higher genus and random matrix descriptions [20], making contact with the black hole information paradox in its various incarnations [21, 22, 24]. Following [20], the amplitude MβM (s1, s2) can be interpreted as a matrix element of operators in the dual boundary theory between energy eigenstates We interpret this result as an exact expression for the gravitational dressing by Liouville gravity of boundary correlators (notice that the boundary lengths are not necessarily large and this corresponds to gravity in a finite spacetime region). We review the exact result presented in [29, 37] for the n boundary-loop correlator at genus zero for the minimal string theory and discuss its decomposition in terms of gluing measures, bulk one-point functions and quantum deformed WP volume factors. For the multi-boundary story for unoriented surfaces, we compute the crosscap spacetime contribution, which we show matches with a GOE/GSE matrix model calculation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
