Worldsheet instanton and string duality
Project/Area Number  10640253 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
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 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1999 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  Superstring theory / σ model / CalabiYau string theory / modular invariance / ADE classification / topological string theory / instanton / virasoro algebra / 超弦理論 / シグマ模型 / カラビ・ヤウ多様体 / モジュラー不変性 / ADE分類 / 位相的弦理論 / インスタントン / ビラソロ代数 / ブラックホール 
Research Abstract 
In 1997 Eguchi, together with Hori and Xiong studied the topological string theory on a target space M and obtained an infinite sequence of differential operators which form a Viarsoro algebra with a central charge c = X(M) (X(M) denotes the Euler number of M). In 1998 Eguchi, together with Jinzenji and Xiong studied the free field realization of Virasoro operators and have shown that there exist a bosonic (fermionic) free field in 1+1 dimension for each even (odd) cohomology class of M. Eguchi together with Xiong further derived topological recursion relations valid in any genus using the result of 2dimensional gravity and verified that the Viraosoro operators predict the correct nunber of holomorphic curves also in genus 2, 3. These results are now called Virasoro conjecture of quantum cohomology. It is wellknown in string theory that the geometry of CalabiYau manifold may be described by LandauGinzburg theory (CY/LG correspondence). In the gauged linear (σ model it is possible to interpole between the regime of the classical geometry of a target manifold and the regime of local geometry of extrema of some superpotential by varying its parameter. 1999 Eguchi together with Jinzenji studied CY/LG correspondence and have shown that the correspondence holds even when M is not a CalabiYau manifold as far as it is a spin manifold. When the CalabiYau manifold degenerates and some of its cycle vanishes, there occur nonperturbative phenomena in string theory like gauge symmetry enhancement. Thus the analysis of string theory in singular CalabiYau manifold is of particular interest. Eguchi together with Sugawara studied the string propagation on singular CalabiYau manifolds and explicitly constructed modular invariant partition functions. Modular invariants are classified according the ADE pattern of isolated sigularities.

Report
(4results)
Research Output
(14results)