Condensable Defects in 4D Dijkgraaf-Witten Models
演讲者
Hao Xu
时间
2025年04月01日 16:00 至 18:00
地点
A3-1-301
线上
Zoom 468 248 1222
(BIMSA)
摘要
Given a finite symmetry group $G$ with anomaly $\pi \in \mathrm{H}^4(G,U(1))$, the 4D Dijkgraaf–Witten model provides an exactly solvable gauge theory with applications in high-energy physics and topological phases of matter. The topological defects in these models form a braided fusion 2-category $\mathscr{Z}(\mathbf{2Vect}^\pi_G)$, the Drinfeld center of $\pi$-twisted $G$-crossed finite semisimple linear categories.
Extending the theory of anyon condensation in 3D, my work (in collaboration with Décoppet) develops a higher-dimensional framework using étale algebras and their local modules in braided fusion 2-categories. In particular, I classify connected étale algebras in $\mathscr{Z}(\mathbf{2Vect}^\pi_G)$, which correspond to twisted $G$-crossed braided multifusion categories.
Additionally, Décoppet has shown that the Drinfeld center of any fusion 2-category is either a 4D Dijkgraaf–Witten model or a fermionic analogue. Time permitting, I will also discuss classification results for fusion 2-categories via the study of Lagrangian algebras.
Extending the theory of anyon condensation in 3D, my work (in collaboration with Décoppet) develops a higher-dimensional framework using étale algebras and their local modules in braided fusion 2-categories. In particular, I classify connected étale algebras in $\mathscr{Z}(\mathbf{2Vect}^\pi_G)$, which correspond to twisted $G$-crossed braided multifusion categories.
Additionally, Décoppet has shown that the Drinfeld center of any fusion 2-category is either a 4D Dijkgraaf–Witten model or a fermionic analogue. Time permitting, I will also discuss classification results for fusion 2-categories via the study of Lagrangian algebras.