RG Flows with Global Symmetry Breaking and Bounds from Chaos

TL;DR

This paper explores the structure of 4d RG flows with broken global symmetries using Nambu-Goldstone bosons, dual CFT descriptions, and chaos bounds to derive constraints and new C-functions.

Contribution

It introduces a novel framework connecting 4d RG flows with symmetry breaking to 3d chaos bounds via holographic duality and spectral deformations.

Findings

Derived low-energy effective actions from symmetry principles.

Established monotonic C-functions constrained by chaos bounds.

Linked 4d RG flow properties to 3d out-of-time-order correlators.

Abstract

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.