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Hirotaka Irie

2011-06-03
10:30:00 - 12:00:00

R102 , Astronomy and Mathematics Building

The multi-cut matrix models are proposed to describe non-critical version of M theory which unifies various solvable string theories in two-dimension. A non-perturbative construction is given by k x k matrix type isomonodromy systems with k tending to infinity. In this talk, we first give a brief introduction of physical motivation, and then concentrate on two types of physically interesting k x k matrix systems. In particular, we discuss how to control the Stokes phenomena in the higher k cases. Explicit solutions for general k which generalize Hastings-McLeod solutions of the Painlev'e II equation are shown to be classified by using Young diagram technique. We also comment on the further generalization to the higher Poincar'e index.