Necessary Condition for Emergent Symmetry from the Conformal Bootstrap.
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap.
复制标题
来自共形自举的紧急对称性的必要条件。
DOI：
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发表时间：
2016
影响因子：
8.6
通讯作者：
T. Ohtsuki
中科院分区：
文献类型：
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作者：
Y. Nakayama;T. Ohtsuki
我们使用共形引导程序来推导出从离散对称性中涌现对称性增强的必要条件（例如，Z_{n}）到连续对称（例如，U（1）]下的重正化群流。在三维情况下，为了使Z 2对称性增强为U 1对称性，共形Bootstrap程序预言序参量场在红外共形不动点处的标度维数必须满足Δ 1>1.08.通过对多个四点函数的同时共形Bootstrap分析，得到了Δ 1>0.580的Z3对称性和Δ 1>0.504的Z4对称性的相似必要条件.作为应用，我们证明了我们的必要条件对QCD中手征相变的性质、Néel价键固体相变中的解禁闭临界性以及临界O（n）模型中的各向异性形变都有严格的约束.我们证明了文献中提出的一些不动点在离散对称性不能禁止的扰动下是不稳定的。在这些情况下，对称性增强的二级相变不会发生。
We use the conformal bootstrap program to derive the necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g., Z_{n}) to continuous symmetry [e.g., U(1)] under the renormalization group flow. In three dimensions, in order for Z_{2} symmetry to be enhanced to U(1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy Δ_{1}>1.08. We also obtain the similar necessary conditions for Z_{3} symmetry with Δ_{1}>0.580 and Z_{4} symmetry with Δ_{1}>0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. As applications, we show that our necessary conditions impose severe constraints on the nature of the chiral phase transition in QCD, the deconfinement criticality in Néel valence bond solid transitions, and anisotropic deformations in critical O(n) models. We prove that some fixed points proposed in the literature are unstable under the perturbation that cannot be forbidden by the discrete symmetry. In these situations, the second-order phase transition with enhanced symmetry cannot happen.