Continuous Categorical Symmetries
演讲者
Ran Luo
时间
2026年05月26日 14:00 至 15:30
地点
A3-3-201
线上
Zoom 559 700 6085
(BIMSA)
摘要
Symmetry categories and SymTFT have become vital tools for studying generalized global symmetries. While this framework is well developed for finite semisimple tensor categories, continuous Lie group symmetries require new methods. In this talk, I will present an operator-algebraic framework for Lie group $G$ symmetry category. The symmetry category is modeled using representations of a $C^*$-algebra of functions on $G$, with anomalies incorporated through bundle-gerbe twists. This gives a continuous analog of ${\rm Vec}_G$ for finite groups. I will then calculate the Drinfeld center of this Lie group symmetry category. It is realized as the representation category of a twisted $C^*$-algebra of the inertia groupoid, with twist given by anomaly transgression. Its simple objects are labeled by conjugacy classes and projective representations of centralizers, same as the case for finite groups. I will conclude with applications to flat gauging Lie group symmetries in the compact real scalar CFT.