三维陈-Simons-物质理论在弦/M-理论、数学物理和凝聚态物理中有着重要的应用。在AdS/CFT对应的框架下，很多超对称陈-Simons-物质理论都有弦/M-理论对偶描述。近年来超对称陈-Simons-物质理论及其弦/M-理论对偶成为了理论物理研究的热点课题。本项目计划研究三维N=4 陈-Simons-物质理论中保持一半超对称的Wilson圈算符的分类问题和若干陈-Simons-物质理论的可积性。这些研究将有助于深入探索三维规范理论和超弦理论的动力学，并有可能发现可积系统的一些最新重要进展在规范理论与超弦理论中的应用。

Three-dimensional Chern-Simons-matter theories have important applications in string/M-theory, mathematical physics and condensed matter physics. In the framework of AdS/CFT correspondence, many supersymmetric Chern-Simons-matter theories have dual description in terms of string/M theory. Recently, supersymmetric Chern-Simons-matter theories and their string/M theory duals become hot research topics in theoretical physics. In this project, we plan to study the classification of BPS Wilson loop operators in three-dimensional N=4 Chern-Simons-matter theories and integrability of some certain Chern-Simons-matter theories. These researches will be helpful for exploring the dynamics of three-dimensional gauge theories and string theory, and may find applications of some recent important progress of integrable systems on gauge theories and string theories.