String Theory and Matrix Models

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In the first half of the academic year of 2002, I made efforts on constructing off-shell boundary and crosscap states and on clarifyning their properties. I collaborated with S.Nakamura and T.Oota to publish two papers.In the second half of 2002, I changed my original plan to investigate physics of gluino condensate in N=1 supersymmetric gauge theory and the proposal of Dijkgraaf-Vafa by developing prepotential theory associated with some Riemann surfaces. I collaborated with A. Morozov to wrote four papers on this subject.In the academic year of 2003, I developed this investigation of N=1 prepotential theory further with H.Kanno. We succeeded in constructing a supereigenvalue model which derives the three Ward-Takahashi relations of supersymmetric gauge theory. We also revealed that the factorization of the matrix model curve is derived from the condition that the determinant of the mixed derivatives of the prepotential vanish. More recently, our current research group at Osaka City University is trying to understand the N=1 prepotential theory from the point of view of partial spontaneous breaking of N=2 supersymmetry.