Holographic and Wilsonian Renormalization Groups

TL;DR

This paper explores the relationship between holographic and Wilsonian renormalization groups, emphasizing the role of multi-trace operators and formulating flow equations, thereby deepening the understanding of RG flows in holographic dualities.

Contribution

It introduces a novel perspective on holographic RG by focusing on multi-trace operators and compares the bulk and boundary RG flows in a new framework.

Findings

Formulation of single- and double-trace flow equations

Highlighting the importance of multi-trace operators in holographic RG

Proposing new directions for understanding the cutoff correspondence

Abstract

We develop parallels between the holographic renormalization group in the bulk and the Wilsonian renormalization group in the dual field theory. Our philosophy differs from most previous work on the holographic RG; the most notable feature is the key role of multi-trace operators. We work out the forms of various single- and double-trace flows. The key question, `what cutoff on the field theory corresponds to a radial cutoff in the bulk?' is left unanswered, but by sharpening the analogy between the two sides we identify possible directions.