A remark on the AdS/CFT correspondence and the renormalization group flow

TL;DR

This paper explores how the AdS/CFT correspondence relates supergravity equations to the renormalization group flow in N=4 SYM theory, especially when deformations are introduced via D3-brane excitations.

Contribution

It proposes that supergravity equations of motion can be interpreted as the renormalization group equations for the dual gauge theory, providing a new perspective on the correspondence.

Findings

Supergravity equations mirror the RG flow in the gauge theory.

Deformations of the conformal theory correspond to higher derivative terms.

The s-wave dilaton example illustrates the proposed interpretation.

Abstract

The correspondence between the four-dimensional SU(N), $\cN = 4$ SYM taken at large $N$ and the type II B SUGRA on the $AdS_5\times S_5$ background is considered. We argue that the classical equations of motion in the SUGRA picture can be interpreted as that of the renormalization group on the SYM side. In fact, when the D3-brane is slightly excited higher derivative terms in the field theory on its world-volume deform it form the conformal $\cN = 4$ SYM limit. We give arguments in favor of that the deformation goes in the way set by the SUGRA equations of motion. Concrete example of the s-wave dilaton is considered.