Theory of TwoDimensional Black Hole
Project/Area Number  05640331 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
素粒子・核・宇宙線

Research Institution  The University of Tokyo 
Principal Investigator 
EGUCHI Tohru The University of Tokyo, graduate school of science, Professor, 大学院・理学系研究科, 教授 (20151970)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

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)

Keywords  String theory / topological / integrable structure / Toda lattice / 弦理論 / 位相的場の理論 / 可積分構造 / 戸田格子 / ミニマル・モデル / 周期積分 / 2次元ブラックホール / Liouville理論 
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 nonlinear sigmamodel can be suitably twisted and converted into a topological field theory, topological sigmamodel. The partition function of the topological sigmamodel 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 1dimensional Toda hierarchy and its partition function can be precisely represented in terms of some largeN matrix integral. The c=1 string theory was originally introduced as an 1dimensional 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 LandauGinzburg 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

Report
(4results)
Research Output
(11results)