Open/Closed String Duality for Topological Gravity with Matter

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.

23 pages, 1 figure, harvmac

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• Computing topological invariants with one and two-matrix models
• On the Connection between N=2 Minimal String and (1,n) Bosonic Minimal String
• Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model
• Noncritical String Correlators, Finite-N Matrix Models and the Vortex Condensate
• Open/closed duality for FZZT branes in c=1
• Topological Open/Closed String Dualities: Matrix Models and Wave Functions
• Analytical approaches to 2D CDT coupled to matter