AI 中文总结
本讲座通过不变量理论推导AdS/CFT对应有限N物理的迹关系影响，明确了无冗余规范不变算子的生成方式及两类不变量的物理解释，为相关研究提供教学式入门。
AI 中文摘要
本讲座为AdS/CFT对应有限N物理的研究提供教学式导论。更具体地说，我们利用不变量理论的强大方法，推导迹关系对规范不变算子空间的影响。核心结论如下：1. 可求解全部迹关系，得到一组无冗余的规范不变算子；2. 该无冗余集合可由两类生成元生成，分别称为初级不变量与次级不变量；3. 初级不变量自然可解释为微扰引力自由度，而次级代数编码对偶引力理论的非微扰效应。
英文摘要
These lectures provide a pedagogical introduction to the study of finite-$N$ physics of the AdS/CFT correspondence. More specifically we develop the consequences of the trace relations for the space of gauge invariant operators, using powerful methods from invariant theory. Our key conclusions are \begin{itemize} \item that the complete set of trace relations can be solved, leaving a non-redundant set of gauge invariant operators, \item that this non-redundant set can be generated using two types of generators, called primary and secondary invariants, and \item that the primary invariants acquire a natural interpretation as perturbative gravitational degrees of freedom, while the secondary algebra encodes non-perturbative effects of the dual gravitational theory. \end{itemize}
Comments64 pages
