Liouville Theory as a 2D Bulk Quantum Gravity Theory and Matrix Models

The aim of this program is to study the case of c=1 Liouville Theory having a dual description in terms of Matrix Quantum Mechanics (MQM) of N-ZZ D0 Branes. Here, instead of the conventional approach, where one interprets Liouville Theory as a worldsheet Conformal Field Theory (CFT, String Theory) embedded in a 2-dimensional target space, we take Liouville Theory as the Quantum Gravity Theory in bulk spacetime. This approach is corroborated by the fact that a holographic connection can be seen as in the case of a single Hermitian matrix model describing (2,p) minimal models coupled to gravity, where the physics of JT-gravity can be reached as a limit of these models. We study the aforementioned theory since it is a richer UV-Complete theory of 2D-gravity with matter. The Matrix Models here do not play the role of their boundary duals, but give a direct link to the third quantized Hilbert Space description, i.e The target space of c=1 string plays the role of the superspace in which these two dimensional geometries are embedded. From the Matrix Model point of view, we introduce appropriate loop operators to create macroscopic boundaries on the bulk geometry. We do this so that the boundary is of fixed size $l$ and is related to the temperature $\beta$ of the holographic dual theory. Here we are currently looking at two-point macroscopic loop operator correlators corresponding to Euclidean wormhole geometry and three-point correlators with a (local) Vertex operator on the same Geometry, which corresponds to the insertion of an operator on the boundary. We initially look at these objects at genus zero and then use MQM to study them at higher genera.