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Hirotaka Irie

2011-11-09
11:00:00 - 12:00:00

400-1 , Mathematics Research Center Building (ori. New Math. Bldg.)

We develop a general framework to study Stokes phenomena of the k x k isomonodromy systems with an arbitrary Poincar\'e index r, especially which correspond to two kinds of physically interesting critical points of the multi-cut two-matrix models. Investigation of this system is important for the purpose of figuring out the non-critical version of M theory which unifies various solvable string theories in two-dimension. In this talk, we mainly discuss the physical boundary conditions on Stokes matrices. We first review the physical motivation of the boundary conditions, and then the physical boundary conditions are then formulated as a connection to the multi-cut two-matrix models. After showing the general multi-cut BC recursion equations, we discuss explicit solutions of the Stokes multipliers for general k and r. We also discuss an interesting connection between the physical boundary conditions and the discrete Hirota dynamics (T-systems) of quantum integrable systems.