A Holographic View on Matrix Model of Black Hole

TL;DR

This paper explores a holographic interpretation of a deformed matrix model related to 2D black holes, establishing a direct connection via Wilson loops and confirming the correspondence through exact computations.

Contribution

It offers a new holographic perspective on the matrix model by interpreting it as gauged quantum mechanics with Wilson loop insertions, providing a more direct mapping to the black hole theory.

Findings

Wilson loop expectation value matches bulk computations

Matrix model corresponds to bosonic SL(2,R)/U(1) theory in genus expansion

Exact '-geometry supports the conjectured duality

Abstract

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.