Callan-Symanzik-like equation in information theory

TL;DR

This paper links holographic complexity growth rate jumps to bulk field dynamics, showing they obey a Callan-Symanzik-like equation, offering a new info-theoretic perspective on scale dependence.

Contribution

It introduces a novel interpretation of the complexity growth rate's behavior near phase transitions through a Callan-Symanzik-like equation in holography.

Findings

CGR exhibits scaling and universality near critical points.

The jumps in CGR are governed by bulk field dynamics.

CGR satisfies a Callan-Symanzik-like equation near transitions.

Abstract

Within the "complexity=anything" proposal of holography, the complexity growth rate (CGR) can exhibit jumps, interpreted as phase transitions. We demonstrate that the location and amplitude of these jumps are governed by the dynamics of bulk fields, which, via the fluid-gravity correspondence, map to the boundary energy-momentum tensor. The behavior of the CGR near these critical points exhibits scaling and universality. We show that the CGR satisfies a Callan-Symanzik-like equation near the transitions. Our results provide a new information-theoretic interpretation of the Callan-Symanzik equation, with the CGR running with the energy scale.