Anatomy of Two Holographic Renormalization Group Flows

TL;DR

The paper advances holographic understanding of two distinct holographic RG flows in D=5 ${ m N}=8$ gauged supergravity: the GPPZ operator deformation and the Coulomb-branch vacuum. By restricting to the ${ m SO}(3)$-invariant sector, the authors derive and solve universal fluctuation equations for the gravity multiplet and two hypermultiplets, revealing three distinct spectra corresponding to the anomaly multiplet, the Lagrangian multiplet, and the active hypermultiplet. A key finding is the universality of the TT graviton sector, which can be expressed through an auxiliary massless scalar, and the generic graviphoton mass relation $m_B^2=-2A''(r)$, with the vector sector behaving differently depending on whether $R$-symmetry is preserved or broken. The work shows that operator deformations and Coulomb-branch deformations yield qualitatively different spectral structures (discrete versus continuous with a mass gap) and clarifies how bulk multiplets map to boundary anomaly multiplets under broken conformal and $R$-symmetries. These results deepen the bulk–boundary dictionary for SUSY-preserving holographic flows and inform the extraction of boundary correlation functions from bulk fluctuations.

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.