String Theory and Statistical Manybody Systems
Project/Area Number  01540233 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  University of Tokyo 
Principal Investigator 
KAZAMA Yoichi University of Tokyo, College of General Arts and Sciences Associate Professor, 教養学部, 助教授 (60144317)

CoInvestigator(Kenkyūbuntansha) 
ICHINOSE Ikuo University of Tokyo, College of General Arts and Sciences Assistant, 教養学部, 助手 (20159841)

Project Fiscal Year 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1990 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1989 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  String Theory / Conformal Field Theory / KacMoody Algebra / Feigin Fuchs Representation / Topological Field Theory / High TALL_c Superconductivity / tJ Model / Nonlinear Sigma Model / 弦理論 / 共形場理論 / KacーMoody代数 / FeiginーFuchs表示 / トポロジカルな場の理論 / 高温超伝導 / tーJモデル / 非線形シグマモデル / KacMoody代数 / FeiginFuchs表示 / ハバドモデル 
Research Abstract 
In this research project, we studied using field theoretical techniques the intimatelyelated structures of string theory and statistical manybody system at criticality and obtained the following results : 1. String theories can be considered as conformally invariant field theories (CFT's) on the string world sheet. A promising framework capable of describing various CFT's comprehensively is the freefield realization introduced by Feigin and Fuchs. We have succeeded in constructing such realizations for the su (n) KacMoody algebras and the associated parafermionic systems which are of fundamental importance. 2. To clarify the relations among various string theories, it is important to study the whole set of two dimensional field theories including gravitational degree of freedom. Recently the exact solution of two dimensional quantum gravity has been obtained by the matrix model approach and moreover the same results can be reproduced by the method of topological field theories (TFT's) which are conceptually quite distinct. We have proposed a formulation of TFT's possessing conformal symmetry and found novel closed algebraic structures of interest. 3. Antiferromagnetic (AF) long range order is considered a key concept in unraveling the high TALL_c superconductivity. We have shown that the OMICRON (3) nonlinear sigma model provides the effective description of the longdistance behavior of the AF Heisenberg model and analyzed it field theoretically. Weak dependence on the three dimensionality has also been studied. 4. Doped high TALL_c superconductor can be described by the tJ model. We analyzed its effective theory, the RHO^1 model, and obtained results on the phase structure, transition temperature, etc., which are in good agreement with experiments. We also found the occurrence of holepair condensation and proposed that this serves as the main mechanism of high TALL_c superconductivity.

Report
(4results)
Research Output
(23results)