| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1994: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1993: ¥700,000 (Direct Cost: ¥700,000)
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| Research Abstract |
Topolgical field theory is an attempt at understanding the geometrical principles behind the string theory and is currently under active investigations. It is known that an N=2 supersymmetric non-linear sigma-model can be suitably twisted and converted into a topological field theory, topological sigma-model. The partition function of the topological sigma-model is given by the sum over holomorphic maps onto some target space and in general difficult to evaluate. Eguchi, together with S.K.Yang, studied the topological CP^1 model on an arbitrary Riemann surfaces and have shown that the integrable structure of the system is described by the 1-dimensional Toda hierarchy and its partition function can be precisely represented in terms of some large-N matrix integral.
The c=1 string theory was originally introduced as an 1-dimensional matrix quantum mechanics and has further been studied extensively using the moethod of collective coordinates, free fermions etc.. Recently an interpretation of the c=1 string theory as a topological field theory has been proposed and a Landau-Ginzburg description has been introduced. Eguchi, together with H.Kanno, studied this proposal and have shown that the integrable structrue of the theory is given by the Toda lattice hierarchy with a special constraint condition being imposed.
Eguchi, togetehr with Y.Yamada and S.K.Yang, studied the higher genus structure of the topological string theory based on the analysis of the higher order corrections to the flow equations. It was shown that there are models of topological string theories which are cosistent at genus g=0 and 1 but can not be extended into higher genera g<greater than or
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