Anatomy of Two Holographic Renormalization Group Flows

TL;DR

This paper analyzes fluctuation equations around two domain wall solutions in 5D gauged supergravity, revealing distinct spectra and symmetry properties of dual field theories related to N=4 SYM deformations.

Contribution

It derives and solves fluctuation equations for two holographic RG flows, elucidating their spectra and symmetry features, and contrasts their behaviors in a unified framework.

Findings

Distinct glueball spectra for different deformations

Continuous spectrum with a mass gap in Coulomb branch flow

Universal features of fluctuation equations and solutions

Abstract

We derive and solve a subset of the fluctuation equations about two domain wall solutions of D=5, N=8 gauged supergravity. One solution is dual to D=4, N=4 SYM theory perturbed by an N=1, SO(3)-invariant mass term and the other to a Coulomb branch deformation. In the first case we study all SO(3)-singlet fields. These are assembled into bulk multiplets dual to the stress tensor multiplet and to the N=1 chiral multiplets Tr Phi^2 and Tr W^2, the former playing the role of anomaly multiplet. Each of these three multiplets has a distinct spectrum of "glueball" states. This behavior is contrasted with the Coulomb branch flow in which all fluctuations studied have a continuous spectrum above a common mass gap, and spontaneous breaking of conformal symmetry is driven by a bulk vector multiplet. R-symmetry is preserved in the field theory, and correspondingly the bulk vector is dual to a linear anomaly multiplet. Generic features of the fluctuation equations and solutions are emphasized. For example, the transverse traceless modes of all fields in the graviton multiplet can be expressed in terms of an auxiliary massless scalar, and gauge fields associated with R-symmetry have a universal effective mass.