String Theory and Statistical Many-body Systems

在本研究项目中，我们利用场论技术研究了弦理论和统计多体系统在临界点的紧密联系结构，得到了以下结果：1.弦理论可以看作弦世界表上的共形不变场理论(CFT)。由Feigin和Fuchs提出的自由场实现是一种能够全面描述各种CFT的框架。我们已经成功地构造了具有重要意义的SU(N)Kac-Moody代数及其相关的准费米子系统的这种实现。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一整套二维场理论是很重要的。最近，用矩阵模型方法得到了二维量子引力的精确解，而拓扑场论方法(TFT‘s)也得到了同样的结果，而拓扑场理论在概念上是完全不同的。我们提出了一种具有共形对称性的TFT的公式，并发现了新的感兴趣的闭合代数结构。反铁磁(AF)长程有序被认为是解开高TALC超导电性的关键概念。我们证明了Omicron(3)非线性Sigma模型能有效地描述AF-Heisenberg模型的长程行为，并从理论上分析了它的场。对三个维度的弱依赖性也进行了研究。掺杂的高TALC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、相变温度等与实验相一致的结果。我们还发现了空穴对凝聚的发生，并提出这是高TALL_c超导电性的主要机制。

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.