Non-SUSY DW's in ISO(7) gauged supergravity

TL;DR

This work analyzes non-supersymmetric domain walls in the SU(3) invariant sector of 4D ISO(7) gauged maximal supergravity, a theory arising from massive IIA on S^6. Using fake supergravity and the Hamilton-Jacobi formalism, it constructs new non-SUSY DWs interpolating between AdS vacua and examines holographic quantities such as the free energy and operator dimensions along RG flows. The study also discusses positive-energy theorems for non-SUSY vacua, the stability of selected AdS points, and the limitations imposed by monotonicity of the fake superpotential on DW connectivity. The results provide a structured DW network linking multiple AdS extrema and offer holographic tests (e.g., bootstrap) to assess possible non-SUSY holography in this string-derived setup.

Abstract

We consider 4D maximal $\mathrm{ISO}(7)$ gauged supergravity, which is known to arise from a consistent truncation of massive IIA supergravity on a six-sphere. Within its $\mathrm{SU}(3)$ invariant sector, the theory is known to possess eight AdS vacua, preserving various amounts of residual supersymmetry and bosonic symmetry. By making use of fake supergravity and the Hamilton-Jacobi formalism, we find novel non-supersymmetric domain walls (DW) interpolating between different pairs of AdS extrema. We conclude by discussing some holographically relevant quantities such as the free energy and the anomalous dimensions of the operators triggering the dual RG flows.

Figures (8)

• Figure 1: The profile of the scalar potential of $\mathrm{SU}(3)$ invariant $\mathrm{ISO}(7)$ gauged supergravity (grey surface), against three globally bounding functions $-3f^2$, obtained by solving the PDE \ref{['PDE_f']} through a perturbative expansion around the three critical points with $\mathrm{SU}(3)$ residual symmetry.
• Figure 2: Domain wall net of the SU(3) invariant sector. Each pair of boxes connected by a line represents a pair of AdS critical points connected by a DW. The colors match the colors used in Table.\ref{['Table:Mass_spectra']} to label the modes triggered for the corresponding DW. Equivalently, a color labels the fake superpotential $f$ used to integrate the flow equations.
• Figure 3: Profiles of the fields $(t,\tau,s,\sigma)$ for all eight DWs colored in Figure \ref{['DWmap']}. Notice some DWs originate from the same fake superpotential but correspond to different boundary conditions according to the different AdS vacua they interpolate between.
• Figure 4: Profiles of the fields for the DW SU(3) $\&~\mathcal{N}=1$$\rightarrow$ SO(7)$_+$ (a) and trajectories of this DW (in purple although it uses the green fake superpotential) and of the SU(3) $\&~\mathcal{N}=1$$\rightarrow$ SO(7)$_+$ (green) and SO(6)$_+$$\rightarrow$ SO(7)$_+$ (red) in the 2D-slice of the scalar manifold that contains these vacua.
• Figure 5: Evolution of the modes along the DWs ending in SO(7)$_+$ ((a) and (b)) and the DW: SU(3) $\&~\mathcal{N}=1$$\rightarrow$ SU(3)$_1$ ($\mathcal{N}=0$)