Stokes phenomena and non-perturbative completion in the multi-cut two-matrix models

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• 作者：Chuan-Tsung Chan^a ; ^{ctchan@thu.edu.tw} ; Hirotaka Irie^b ; ^c ; ^{irie@phys.cts.nthu.edu.tw} ; ^{irie@phys.ntu.edu.tw} ; Chi-Hsien Yeh^b ; ^{d95222008@ntu.edu.tw}
• 刊名：Nuclear Physics B
• 出版年：2012
• 期刊代码：45_05503213
• 类别：ph
• 出版时间：1 January, 2012
• 卷：854
• 期：1
• 页码：67-132
• 文件大小：1873 K

摘要

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 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 case (pure-supergravity case) completely fixes the D-instanton chemical potentials and results in the Hastings-McLeod solution to the Painlev茅 II equation. It is also stressed that the Riemann-Hilbert approach realizes an off-shell background independent formulation of non-critical string theory.