A Holographic View on Matrix Model of Black Hole

We investigate a deformed matrix model proposed by Kazakov et.al. in relationto Witten's two-dimensional black hole. The existing conjectures assert theequivalence of the two by mapping each to a deformed c=1 theory called thesine-Liouville theory. We point out that the matrix theory in question may benaturally interpreted as a gauged quantum mechanics deformed by insertion of anexponentiated Wilson loop operator, which gives us more direct and holographicmap between the two sides. The matrix model in the usual scaling limit mustcorrespond to the bosonic SL(2,R)/U(1) theory in genus expansion but exact in\alpha'. We successfully test this by computing the Wilson loop expectationvalue and comparing it against the bulk computation. For the latter, we employthe \alpha'-exact geometry proposed by Dijkgraaf, Verlinde, and Verlinde, whichwas further advocated by Tseytlin. We close with comments on open problems.Comment: LaTeX, 19 page