Notes on the algebraic curves in (p,q) minimal string theory

Abstract

Loop amplitudes in (p,q) minimal string theory are studied in terms of the continuum string field theory based on the free fermion realization of the KP hierarchy. We derive the Schwinger-Dyson equations for FZZT disk amplitudes directly from the W_{1+\infty} constraints in the string field formulation and give explicitly the algebraic curves of disk amplitudes for general backgrounds. We further give annulus amplitudes of FZZT-FZZT, FZZT-ZZ and ZZ-ZZ branes, generalizing our previous D-instanton calculus from the minimal unitary series (p,p+1) to general (p,q) series. We also give a detailed explanation on the equivalence between the Douglas equation and the string field theory based on the KP hierarchy under the W_{1+\infty} constraints.

61 pages, 1 figure, section 2.5 and Appendix B added, references added, final version to appear in JHEP

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Cited by in corpus (13)

• Quantum Curves and D-Modules
• Minimal Open Strings
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• A string field theoretical description of (p,q) minimal superstrings
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• T-duality of ZZ-brane
• Fractional supersymmetric Liouville theory and the multi-cut matrix models
• Macroscopic loop amplitudes in the multi-cut two-matrix models
• Notes on D-branes and dualities in (p,q) minimal superstring theory
• Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories
• Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory
• Analytic Study for the String Theory Landscapes via Matrix Models
• Wronskians, dualities and FZZT-Cardy branes