Nonperturbative methods in quantum field theory

最近，用于处理量子场论的非摄动方面的数学方法有了重要的发展。诸如高形式对称、广义t - Hooft异常、高群结构等主题正在成为理解量子场论各种结构的不可或缺的工具。本文将着重于使用这些技术来分析强耦合规范理论。分析将包括真空结构、扩展对象（例如，畴壁和弦）、复合材料和强耦合理论中的凝聚物的研究。

Recently, there have been important developments in the mathematical methods used to tackle the nonperturbative aspects of quantum field theories. Topics such as higher-form symmetries, generalized 't Hooft anomalies, higher-group structures, etc. are becoming indispensable tools to understand various structures of quantum field theories. The thesis will focus on using these techniques to analyze strongly-coupled gauge theories. The analysis will include the study of vacuum structure, extended objects (e.g., domain walls and string), composites, and condensates in strongly-coupled theories.