Hao Zheng

Liang Kong

Tuesday, September 27, 2022 1:30 PM - 3:00 PM

1131

Tencent 607 3645 0351 ()

I will explain a new type of holographic dualities between n+1D topological orders with a chosen boundary condition and nD (potentially gapless) quantum liquids. It is based on the idea of topological Wick rotation, a notion which was first used in arXiv:1705.01087 and was named, emphasized and generalized later in arXiv:1905.04924. I will provide some explicit examples in low dimensions, including the duality between 2+1D toric code model and 1+1D Ising chain and its finite-group generalizations (independently obtained by Freed and Teleman arXiv:1806.00008); that between 2+1D topological orders and 1+1D rational conformal field theories. As a consequence, we immediately obtain the classification of all 1+1D gapped quantum phases, a result which was obtained previously via a very different approach. This classification result generalizes to gapped quantum liquids in higher dimensions (with more general symmetries). I will also discuss some generalizations of this holographic duality and its relation to AdS/CFT duality.

Liang Kong is a mathematical physicist at the Shenzhen International Quantum Academy. His research focuses on topological quantum field theory, two-dimensional conformal field theory, category theory, representation theory, and topological phases of matter. He received his B.S. in Physics from the University of Science and Technology of China, his M.S. in Physics from the University of Houston, and his Ph.D. in Mathematics from Rutgers University. He subsequently held research positions at the Max Planck Institute for Mathematics, the Institut des Hautes Études Scientifiques (IHÉS), and the California Institute of Technology. He later held positions at the Institute for Advanced Study at Tsinghua University, the University of New Hampshire, Harvard University’s Center of Mathematical Sciences and Applications, the Yau Mathematical Sciences Center at Tsinghua University, and the Institute for Quantum Science and Engineering at the Southern University of Science and Technology. He joined the Shenzhen International Quantum Academy in 2025.