论文标题
RG流动，全球对称性破裂和混乱的界限
RG Flows with Global Symmetry Breaking and Bounds from Chaos
论文作者
论文摘要
我们讨论了紫外线中的连续全局对称性损坏的重新归一化组（RG）流的一般方面（RG）流量。每个这样的RG流都可以用Nambu-goldstone玻色子的动力学来描述，这些玻色子的损坏了保形和全局对称性。我们得出了低能量的有效作用，该动作描述了这类RG流从基本的对称原理中。我们将Nambu-Goldstone玻色子的理论视为具有平坦空间极限的反DE保姆空间中的理论。这使得根据广义免费CFT $ _3 $的光谱变形，可以实现这些4D RG流的等效CFT $ _3 $公式。我们利用这对双重描述来对与4D中的单一RG流相关的低能有效作用施加进一步的限制，通过调用3D中的混乱。这种方法自然地提供了一组独立的单调降低4D RG流的$ C $函数，通过将4D $ C $函数与某些诊断3D诊断混乱的某些超时相关器明确关联，并通过将4D $ C $函数与某些超时相关器联系起来。我们还评论了QFT中RG和混乱之间更一般的联系。
We discuss general aspects of renormalization group (RG) flows between two conformal fixed points in 4d with a broken continuous global symmetry in the UV. Every such RG flow can be described in terms of the dynamics of Nambu-Goldstone bosons of broken conformal and global symmetries. We derive the low-energy effective action that describes this class of RG flows from basic symmetry principles. We view the theory of Nambu-Goldstone bosons as a theory in anti-de Sitter space with the flat space limit. This enables an equivalent CFT$_3$ formulation of these 4d RG flows in terms of spectral deformations of a generalized free CFT$_3$. We utilize this dual description to impose further constraints on the low energy effective action associated with unitary RG flows in 4d by invoking the chaos bound in 3d. This approach naturally provides a set of independent monotonically decreasing $C$-functions for 4d RG flows with global symmetry breaking by explicitly relating 4d $C$-functions with certain out-of-time-order correlators that diagnose chaos in 3d. We also comment on a more general connection between RG and chaos in QFT.
