Hu Liangdong, He Yin-Chen, Zhu W
Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China.
Department of Physics, School of Science, Westlake University, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China.
Phys Rev Lett. 2023 Jul 21;131(3):031601. doi: 10.1103/PhysRevLett.131.031601.
Conformal field theory (CFT) plays a crucial role in the study of various critical phenomena. While much attention has been paid to the critical exponents of different universalities, which correspond to the conformal dimensions of CFT primary fields, other important and intricate data such as operator product expansion (OPE) coefficients governing the fusion of two primary fields, have remained largely unexplored, especially in dimensions higher than 2D (or equivalently, 1+1D). Motivated by the recently proposed fuzzy sphere regularization, we investigate the operator content of 3D Ising criticality from a microscopic perspective. We first outline the procedure for extracting OPE coefficients on the fuzzy sphere and then compute 13 OPE coefficients of low-lying CFT primary fields. Our results are highly accurate and in agreement with the numerical conformal bootstrap data of 3D Ising CFT. Moreover, we were able to obtain 4 OPE coefficients, including f_{T_{μν}T_{ρη}ε}, which were previously unknown, thus demonstrating the superior capabilities of our scheme. Expanding the horizon of the fuzzy sphere regularization from the state perspective to the operator perspective opens up new avenues for exploring a wealth of new physics.
共形场论（CFT）在各种临界现象的研究中起着至关重要的作用。虽然人们对不同普适性的临界指数给予了很多关注，这些指数对应于CFT原初场的共形维度，但其他重要且复杂的数据，如控制两个原初场融合的算符乘积展开（OPE）系数，在很大程度上仍未得到充分探索，特别是在高于二维（或等效地，1 + 1维）的维度中。受最近提出的模糊球正则化的启发，我们从微观角度研究三维伊辛临界性的算符内容。我们首先概述在模糊球上提取OPE系数的过程，然后计算低能CFT原初场的13个OPE系数。我们的结果高度精确，并且与三维伊辛CFT的数值共形引导数据一致。此外，我们能够获得4个OPE系数，包括之前未知的$f_{T_{μν}T_{ρη}ε}$，从而证明了我们方案的卓越能力。将模糊球正则化的视野从态的角度扩展到算符的角度，为探索大量新物理开辟了新途径。
