Module Category and Symmetry-TFT

by Toshinori TAKAMA (YITP)

Wednesday 19 Nov 2025, 13:30 → 16:30 Asia/Tokyo

This seminar will be held in Japanese.

Zoom Link

https://us06web.zoom.us/j/84516625657?pwd=FxpK1CtZb3jYNE1Pb5baZ3RJx2FduO.1

Meeting ID: 845 1662 5657
Passcode: 061558

Abstruct

Generalized symmetry in field theory can be realized using gapped boundary conditions of a topological field theory (TFT) one dimension higher. This TFT is called a Symmetry-TFT.

In this talk, we confirm using concrete examples that the Symmetry-TFT realizing non-invertible symmetry in 1+1 dimensions is the 2+1-dimensional Turaev-Viro TFT. Furthermore, we show that the gapped boundary conditions of the Turaev-Viro TQFT constructed from a unitary fusion category $\mathcal{C}$ are classified by the Lagrangian algebra possessed by the Drinfeld center $\mathcal{Z}(\mathcal{C})$ of $\mathcal{C}$, and provide a physical interpretation of this construction.

References

• https://arxiv.org/abs/2209.07471
• https://arxiv.org/abs/2008.08598
• https://arxiv.org/abs/1203.4568
• https://arxiv.org/abs/1009.2117
• P. Etingof, S. Gelaki, D. Nikshych, V. Ostrik, "Tensor Categories", 2015
• V. Turaev, A. Virelizier, "Monoidal Categories and Topological Field Theories", 2017