Non-Perturbative Effects in Matrix Models and D-branes

Abstract

The large order growth of string perturbation theory in $c\le 1$ conformal field theory coupled to world sheet gravity implies the presence of $O(e^{-\frac{1}{g_s}})$ non-perturbative effects, whose leading behavior can be calculated in the matrix model approach. Recently it was proposed that the same effects should be reproduced by studying certain localized D-branes in Liouville Field Theory, which were constructed by A. and Al. Zamolodchikov. We discuss this correspondence in a number of different cases: unitary minimal models coupled to Liouville, where we compare the continuum analysis to the matrix model results of Eynard and Zinn-Justin, and compact c=1 CFT coupled to Liouville in the presence of a condensate of winding modes, where we derive the matrix model prediction and compare it to Liouville theory. In both cases we find agreement between the two approaches. The c=1 analysis also leads to predictions about properties of D-branes localized in the vicinity of the tip of the cigar in SL(2)/U(1) CFT with c=26.

27 pages, lanlmac; minor changes

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• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
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• On Boundary Perturbations in Liouville Theory and Brane Dynamics in Noncritical String Theories
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• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• D-brane Dynamics in the c=1 Matrix Model
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• Boundary Ground Ring in 2D String Theory
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• Matrix integrals $\&$ finite holography
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• The decay of quantum D-branes
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• Nonperturbative Effect in c=1 Noncritical String Theory and Penner Model
• Notes on the algebraic curves in (p,q) minimal string theory
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• Topological B-model and $\hat{c}=1$ String Theory
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• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
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• c-map as c=1 string
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• Analytic Study for the String Theory Landscapes via Matrix Models
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• Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings
• Duality Constraints on String Theory: Instantons and spectral networks
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