Condensation of string-like topological defects in (3+1)d gapped bulk theory

by Dr Hao Xu (Centre for Quantum Mathematics (SDU))

Monday 29 Dec 2025, 10:30 → 11:30 Asia/Shanghai

B105 (CHEP)

 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.

Bio：
I am a postdoctoral researcher in Prof. Apoorv Tiwari's group at the Centre for Quantum Mathematics (SDU). I obtained my doctoral degree from Georg-August-Universität Göttingen, when I was supervised by Prof. Dr. Chenchang Zhu. Before that, I was an undergraduate student at Jesus College, University of Oxford. I am primarily focused on exploring mathematical structures that arise from the topological phases of quantum many-body systems, specifically higher fusion categories. These categories play a fundamental role in understanding the intricate connections between topological quantum field theories (TQFTs), homotopy theory, representation theory and related areas of study.

Tenceng Meeting：863-823-018

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