Quantum Groups as Global Symmetries

ADS seminar

Organizers：

数学物理团队

Speaker：

Jiaxin Qiao

EPFL Lausanne

Time：

Thursday, 13:30

Dec. 26, 2024

Venue：

Qiuzhen Hall, Ningzhai

Title:

Quantum Groups as Global Symmetries

Abstract：

In this talk, I will discuss the general properties of two-dimensional quantum field theories and conformal field theories with the quantum group Uq(sl2) as a global internal symmetry. In such theories, operators are generically non-local and should be thought of as living at the ends of topological lines. I will discuss the constraints on the spacetime spin (for QFTs) and OPE coefficients (for CFTs) imposed by Uq(sl2) Ward identities. Then I will present an example of a Uq(sl2) -symmetric CFT and two ways of solving the theory: the conformal bootstrap and a novel Coulomb gas construction (if time permits). The talk is based on the joint work with Gabai, Gorbenko, Zan and Zhabin [2410.24142, 2410.24143].

Remark: The talk will mostly focus on Uq(sl2) for q not a root of unity. If time permits, I will also discuss the CFT example when q approaches the value of the critical Ising model, where q becomes a root of unity and the CFT becomes logarithmic.