On Integrable c<1 Open--Closed String Theory

Abstract

The integrable structure of open--closed string theories in the $(p,q)$ conformal minimal model backgrounds is presented. The relation between the $\tau$--function of the closed string theory and that of the open--closed string theory is uncovered. The resulting description of the open--closed string theory is shown to fit very naturally into the framework of the $sl(q,\mathrm{C})$ KdV hierarchies. In particular, the twisted bosons which underlie and organise the structure of the closed string theory play a similar role here and may be employed to derive loop equations and correlation function recursion relations for the open--closed strings in a simple way.

(Slight corrections to title, text, terminology and references. Note added. No change in physics.) , 30pp, IASSNS--HEP--93/5

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• D-Branes and Fluxes in Supersymmetric Quantum Mechanics
• Open minimal strings and open Gelfand-Dickey hierarchies
• Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings
• From minimal gravity to open intersection theory
• Unoriented Minimal Type 0 Strings
• Topological Two-Dimensional Gravity on Surfaces with Boundary
• Topological Open/Closed String Dualities: Matrix Models and Wave Functions