Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-26
Nucl.Phys.B854:67-132,2012
Physics
High Energy Physics
High Energy Physics - Theory
71 pages, v3: organization of Sec. 3, Sec. 4, App. C and App. D improved, final version to be published in Nucl. Phys. B
Scientific paper
10.1016/j.nuclphysb.2011.08.021
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 Z_k 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 Painlev\'e II equation. It is also stressed that the Riemann-Hilbert approach realizes an off-shell background independent formulation of non-critical string theory.
Chan Chuan-Tsung
Irie Hirotaka
Yeh Chi-Hsien
No associations
LandOfFree
Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-462695