Liouville theory and Matrix models: A Wheeler DeWitt perspective

Date: 
09/29/2021 - 12:00pm
Location: 
zoom
Speaker(s) / Presenter(s): 
Panagiotis Betzios (UBC)
We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to c = 1 matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravity. Macroscopic loop operators define the asymptotic region on which the holographic boundary dual could be expected to reside. Matrix quantum mechanics and the associated double scaled fermionic field theory, are providing the complete dynamics of such two-dimensional universes with c=1 matter, including the effects of topology change.  On the other hand, if we try to associate a Hilbert space to a single boundary dual living on the loop, it cannot contain all the information present in the non-perturbative bulk quantum gravity path integral and MQM.
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