  We investigate a deformed matrix model proposed by Kazakov et.al. in relation
to Witten's two-dimensional black hole. The existing conjectures assert the
equivalence of the two by mapping each to a deformed c=1 theory called the
sine-Liouville theory. We point out that the matrix theory in question may be
naturally interpreted as a gauged quantum mechanics deformed by insertion of an
exponentiated Wilson loop operator, which gives us more direct and holographic
map between the two sides. The matrix model in the usual scaling limit must
correspond 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 expectation
value and comparing it against the bulk computation. For the latter, we employ
the \alpha'-exact geometry proposed by Dijkgraaf, Verlinde, and Verlinde, which
was further advocated by Tseytlin. We close with comments on open problems.
