Topological Matrix Models, Liouville Matrix Model and c=1 String Theory

TL;DR

This paper reviews matrix models connected to Riemann surface moduli space and c=1 string theory, demonstrating their equivalence and proposing a new Liouville matrix model interpretation related to D-instantons.

Contribution

It introduces a new equivalence between Penner, W-infinity, and Liouville matrix models in the context of c=1 string theory.

Findings

Penner and W-infinity models are equivalent.

These models are also equivalent to a Liouville matrix model.

Potential interpretation in terms of N D-instantons of c=1 string.

Abstract

This is a review of some beautiful matrix models related to the moduli space of Riemann surfaces as well as to noncritical c=1 string theory at self-dual radius. These include the Penner model and the W-infinity model, which have different origins but are equivalent to each other. In the final section, which is new material, it is shown that these models are also equivalent to a Liouville matrix model. We speculate that this might be interpreted in terms of N D-instantons of the c=1 string.