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String Theory and Statistical Many-body Systems

弦理论和统计多体系统

基本信息

批准号：
01540233
负责人：
KAZAMA Yoichi
金额：
$ 1.15万
依托单位：
University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1989
资助国家：
日本
起止时间：
1989 至 1990
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540233/
关键词：
String Theory Conformal Field Theory Kac-Moody Algebra Feigin Fuchs Representation Topological Field Theory High TALL_c Superconductivity t-J Model Non-linear Sigma Model Kac-Moody代数 Feigin-Fuchs表示ハバ-ドモデル

项目摘要

In this research project, we studied using field theoretical techniques the intimatelyelated structures of string theory and statistical many-body 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 free-field realization introduced by Feigin and Fuchs. We have succeeded in constructing such realizations for the su (n) Kac-Moody 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. Anti-ferromagnetic (AF) long range order is considered a key concept in unraveling the high TALL_c superconductivity. We have shown that the OMICRON (3) non-linear sigma model provides the effective description of the long-distance 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 t-J 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 hole-pair condensation and proposed that this serves as the main mechanism of high TALL_c superconductivity.

在本研究项目中，我们用场论方法研究了弦理论和统计多体系统在临界态下的紧密联系结构，得到了以下结果：1.弦理论可以被认为是弦世界表上的共形不变场论。Feigin和Fuchs提出的自由场实现是一个很有前途的框架，它能够全面地描述各种CFT。我们已经成功地构造了su（n）Kac-Moody代数和相关的仿费米子系统的这种实现，这是非常重要的.为了弄清各种弦理论之间的关系，研究包括引力自由度在内的整个二维场论是很重要的。最近，二维量子引力的精确解已经通过矩阵模型方法得到，而且同样的结果可以通过概念上截然不同的拓扑场论（TFT）方法重现。我们提出了一个具有共形对称性的TFT的公式，并发现了新的封闭代数结构。反铁磁长程有序被认为是解释高TALL_c超导性的一个关键概念。我们证明了OMICRON（3）非线性σ模型对AF Heisenberg模型的长距离行为提供了有效的描述，并从理论上分析了它的场。对三维空间的弱相关性也进行了研究.掺杂的高TALL_c超导体可用t-J模型描述。我们分析了它的有效理论RHO ^1模型，得到了相结构、相变温度等方面的结果，与实验结果吻合较好。我们还发现了空穴对凝聚的存在，并认为这是高TALL_c超导性的主要机制。