The study of 2D and 3D topological orders has historically progressed along two parallel paradigms of exactly solvable models: the “group element” basis (encompassing 2D Quantum Double and 3D Gauge Theory models) and the “representation” basis (2D Levin-Wen and 3D Walker-Wang models). In this talk, we establish a rigorous duality between these two frameworks via a finite group Fourier transform. We demonstrate that models based on a gauge group G map exactly to their string-net counterparts — the extended Levin-Wen (HGW) and Walker-Wang models — formulated with the input fusion category Rep(G). Furthermore, by generalizing this Fourier transform to gapped boundaries, we reveal that charge condensations on the boundaries of these topological orders are elegantly described by Frobenius algebras in Rep(G). We conclude by applying this transform to excited states, shedding light on the often-overlooked internal gauge degrees of freedom of anyons.

Biography

王思源，2022年获复旦大学物理系学士学位，现为复旦大学理论物理专业在读博士，导师万义顿教授。主要研究方向为利用拓扑序的严格可解模型研究拓扑序的对称结构和任意子凝聚等现象，在JHEP发表文章两篇，在SciPost Physics发表文章一篇。

Inviter: Hao Song