Open/Closed String Duality for Topological Gravity with Matter

TL;DR

This paper demonstrates an explicit open/closed string duality in topological gravity with matter by computing the FZZT brane partition function via a dual two-matrix model and relating it to the Kontsevich integral.

Contribution

It extends the open/closed string duality framework from pure topological gravity to include matter, using the dual two-matrix model and the generalized Kontsevich integral.

Findings

Explicit computation of FZZT brane partition function for gravity with matter.

Establishment of open/closed string duality in this context.

Clarification of the role of nonperturbative effects and Stokes' phenomenon.

Abstract

The exact FZZT brane partition function for topological gravity with matter is computed using the dual two-matrix model. We show how the effective theory of open strings on a stack of FZZT branes is described by the generalized Kontsevich matrix integral, extending the earlier result for pure topological gravity. Using the well-known relation between the Kontsevich integral and a certain shift in the closed-string background, we conclude that these models exhibit open/closed string duality explicitly. Just as in pure topological gravity, the unphysical sheets of the classical FZZT moduli space are eliminated in the exact answer. Instead, they contribute small, nonperturbative corrections to the exact answer through Stokes' phenomenon.