  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.
