A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model

TL;DR

This paper demonstrates that the Kontsevich matrix model exemplifies exact open/closed duality in topological string theory, connecting open string field theory on stable branes to closed string models at finite N.

Contribution

It establishes a precise link between topological matrix models and open/closed duality, showing the Kontsevich model arises from open string field theory on stable branes.

Findings

Kontsevich model is an example of open/closed duality.

The duality holds at finite N and generic couplings.

The model is derived via topological localization of open string field theory.

Abstract

We argue that topological matrix models (matrix models of the Kontsevich type) are examples of exact open/closed duality. The duality works at finite N and for generic `t Hooft couplings. We consider in detail the paradigm of the Kontsevich model for two-dimensional topological gravity. We demonstrate that the Kontsevich model arises by topological localization of cubic open string field theory on N stable branes. Our analysis is based on standard worldsheet methods in the context of non-critical bosonic string theory. The stable branes have Neumann (FZZT) boundary conditions in the Liouville direction. Several generalizations are possible.