Notes on Multi-Trace Operators and Holographic Renormalization Group

TL;DR

This paper presents a universal formulation of the Holographic Renormalization Group within Quantum Field Theory, using Hamiltonian flow on the space of gauge-invariant operators, with classical dynamics emerging at large N.

Contribution

It introduces a Hamiltonian flow framework for the Holographic Renormalization Group applicable to quantum field theories, emphasizing a universal and geometric approach.

Findings

Holographic RG can be formulated as Hamiltonian flow on the cotangent bundle of gauge-invariant operators.

Classical Hamiltonian dynamics are recovered in the large N limit.

The approach provides a universal QFT-based perspective on holographic renormalization.

Abstract

It is shown that the Holographic Renormalization Group can be formulated universally within Quantum Field Theory as (the quantization of) the Hamiltonian flow on the cotangent bundle to the space of gauge-invariant single-trace operators supplied with the canonical symplectic structure. The classical Hamiltonian dynamics is recovered in the large $N$ limit.