Stokes phenomena and non-perturbative completion in the multi-cut two-matrix models |
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Authors: | Chuan-Tsung Chan Chi-Hsien Yeh |
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Institution: | a Department of Physics, Tunghai University, 40704 Taiwan, ROC b Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan, ROC c National Center for Theoretical Sciences, National Tsing-Hua University, Hsinchu 30013, Taiwan, ROC11The affiliation of H. Irie from January 1st, 2011. |
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Abstract: | The Stokes multipliers in the matrix models are invariants in the string-theory moduli space and related to the D-instanton chemical potentials. They not only represent non-perturbative information but also play an important role in connecting various perturbative string theories in the moduli space. They are a key concept to the non-perturbative completion of string theory and also expected to imply some remnant of strong coupling dynamics in M theory. In this paper, we investigate the non-perturbative completion problem consisting of two constraints on the Stokes multipliers. As the first constraint, Stokes phenomena which realize the multi-cut geometry are studied in the Zk symmetric critical points of the multi-cut two-matrix models. Sequence of solutions to the constraints are obtained in general k-cut critical points. A discrete set of solutions and a continuum set of solutions are explicitly shown, and they can be classified by several constrained configurations of the Young diagram. As the second constraint, we discuss non-perturbative stability of backgrounds in terms of the Riemann-Hilbert problem. In particular, our procedure in the 2-cut (1,2) case (pure-supergravity case) completely fixes the D-instanton chemical potentials and results in the Hastings-McLeod solution to the Painlevé II equation. It is also stressed that the Riemann-Hilbert approach realizes an off-shell background independent formulation of non-critical string theory. |
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