Fast Scrambling under an RG-flow

The notion of information scrambling is tied to the long-time behaviour of a system and therefore is related to its infra-red dynamics. In fast scramblers, information spreads as a logarithmic function of the number of degrees of freedom. Ordinarily, under an RG-flow, scrambling will become faster in the IR since many degrees of freedom are integrated out, as a consequence of the c-theorem. In this article, we consider a class of Holographic quantum field theories (QFT), which are strongly coupled large $N$ gauge theories with large number of adjoint and fundamental matter, in which scrambling slows down in the IR. This happens since more degrees of freedom are inserted in the IR, compared to the UV, in a precise sense. For generic large $N$ gauge theories, we also explore general, perturbative flow features of the corresponding Lyapunov exponent, based on the Callan-Symanzik equation.