李超代数表示与超对称Wess-Zumino-Novikov-Witten模型关联函数

Superalgebras and their corresponding conformal field theories have drastically increased over the last ten years due to their applications in superstring theory and condensed matter physics. By using shift operators, coherent states method, we shall explicitly construct finite dimesional representations of Lie superalgebra D(2,1;a), osp(4|2). Free field realizations of primary fields of associated Wess- Zumino-Novikov-Witten models can be obtained by using the free field representa- tions and finite dimensional representations of Lie superalgebras. Using the free field realizations of primary fields and screening currents one can calculate cor- relation functions of WZNW models. Our results are expected to be useful in the supersymmetric method to quantum disordered systems.

超代数以及与之相对应的共形场论在过去几十年内从超弦理论到凝聚态物理学都得到了巨大的发展。通过利用shift operator、 coherent states method，申请者将构造李超代数 D(2,1;a), osp(4|2）的明显表达式。利用李超代数的有限维表示与自由场实现可以构造出相应的Wess-Zumino-Novikov-Witten模型的初级场的自由场表示。利用初级场和屏蔽流的自由场表示即可以求解WZNW模型的关联函数。申请者的研究结果预期将对超对称化方法研究量子无序系统有重要作用。