Boundary Correlators in 2D Quantum Gravity: Liouville versus Discrete Approach

by Kostov, Ivan

Abstract

We compare the world-sheet approach to 2D quantum gravity based on Liouville theory and target-space approach, based on matrix models. In the latter approach the matter field is realized as loop gas on random planar graph. We calculate the two-point boundary correlation function on a disc and show that the world-sheet and the target-space approaches lead to the same result, up to a constant factor. The loop equation for the two-point function that follows from the loop gas representation is equivalent to the functional equation obtained using the fusion rules in Liouville theory.

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