arXiv 2012.104502020-12hep-thcond-mat.str-elhep-phquant-ph

全局对称破缺的RG流与混沌边界

RG Flows with Global Symmetry Breaking and Bounds from Chaos

Sandipan Kundu

备注：: 39 pages + appendices, multiple figures

摘要：

本文讨论了四维空间中两个共形不动点之间的重整化群（RG）流的一般性质，其中UV空间中的连续对称性被破缺。每一个这样的RG流可以被描述的动力学的破坏共形和全球对称性的南武-戈德斯通玻色子。我们从基本的对称性原理推导出描述这类RG流的低能有效作用。我们把Nambu-Goldstone玻色子理论看作是具有平坦空间极限的反德西特空间中的理论。这使得这些4d RG流的等效CFT $_3$公式能够在广义自由CFT $_3$的谱变形方面。我们利用这种双重的描述施加进一步的约束与酉RG流在4D的低能量有效的行动，通过调用在3D的混沌界。这种方法自然地提供了一组独立的单调递减的$C$ -功能的4D RG流与全球对称性破缺明确相关的4D $C$ -功能与一定的时间顺序诊断混沌在3D。我们还评论RG和QFT中的混沌之间的更一般的连接。

英文摘要：

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.

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