2024/10/31 by Barak Gabai, Gabai, Barak, V. Gorbenko +7 · 3 citations
Physics and Astronomy · Social Sciences · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #International Science and Diplomacy #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2410.24142
openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the 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.