论文标题
在$ 3D $ ising过渡中揭示了共形对称性：来自模糊球体正则化的状态操作员对应关系
Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization
论文作者
论文摘要
$ 3D $ ising的过渡是本质上最著名，最尚未解决的关键现象，长期以来一直猜想具有紧急的保形对称性，类似于$ 2D $ ising Transition的情况。然而，很少直接探索$ 3D $ ising过渡中保形不变性的出现，这主要是由于不可避免的数学或概念性障碍。在这里，我们设计了一种创新的方式来研究球形几何的$ 3D $ ising相变的量子版本，并使用“模糊（非交通）球体”正则化。我们准确地计算和分析了过渡时的能量光谱，并明确证明了状态操作员对应关系（即径向量化），这是保形场理论的指纹。特别是，我们已经确定了高精度内的13个平均数量 - 偶然性运算符，还有2个以前尚不清楚的奇偶校验运算符。我们的结果直接阐明了$ 3D $ ising Transition的紧急形式对称性，这是Polyakov半个世纪前的猜想。更重要的是，我们的方法通过使用国家操作员对应关系和球形几何形状来开辟一条新的途径，以研究$ 3D $ CFTS。
The $3D$ Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the $2D$ Ising transition. Yet, the emergence of conformal invariance in the $3D$ Ising transition has rarely been explored directly, mainly due to unavoidable mathematical or conceptual obstructions. Here, we design an innovative way to study the quantum version of the $3D$ Ising phase transition on spherical geometry, using the "fuzzy (non-commutative) sphere" regularization. We accurately calculate and analyze the energy spectra at the transition, and explicitly demonstrate the state-operator correspondence (i.e. radial quantization), a fingerprint of conformal field theory. In particular, we have identified 13 parity-even primary operators within a high accuracy and 2 parity-odd operators that were not known before. Our result directly elucidates the emergent conformal symmetry of the $3D$ Ising transition, a conjecture made by Polyakov half a century ago. More importantly, our approach opens a new avenue for studying $3D$ CFTs by making use of the state-operator correspondence and spherical geometry.
