We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, given by Ward identities, that correlation functions of the theory should satisfy. We also show that generators of the symmetry can be represented by topological lines with some novel properties. We then discuss a particular example of Uq (sl2) symmetric CFT, which we solve using bootstrap techniques and relying on the symmetry. We finally show strong evidence that for a special value of q a subsector of this theory reproduces the fermionic formulation of the Ising model. This suggests that a quantum group can act on local operators as well, however, it generically transforms them into non-local ones.
Biography:
Jiaxin Qiao is currently a postdoctoral researcher at EPFL. Prior to this, he received his PhD in Physics from École Normale Supérieure de Paris - PSL in 2022, his MSc in Physics from École Normale Supérieure de Paris in 2019, and his BSc in Physics from Peking University in 2016.
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Prof. Yinan Wang