Holographic solutions from 5D $SO(2)\times ISO(3)$ $N=4$ gauged supergravity

TL;DR

This work analyzes holographic solutions in five-dimensional $N=4$ gauged supergravity with gauge group $SO(2)\times ISO(3)$, derived from a seven-dimensional theory on a Riemann surface and yielding a supersymmetric $AdS_5$ vacuum dual to an $N=2$ SCFT from M5-branes on $H^2$. The authors construct holographic RG flows, Janus interfaces, and supersymmetric $AdS_5$ black strings and black holes, characterizing their UV/IR structure, BPS equations, and uplift to M-theory on $H^2\times S^4$. They find flows to non-conformal IR phases in several symmetry sectors, analyze the presence or absence of $AdS_3$ or $AdS_2$ near-horizon geometries, and compute central charges and entropies for the dual two-dimensional SCFTs and quantum mechanics, with all solutions admitting eleven-dimensional uplifts. The results illustrate twisted compactifications and dimensional reduction patterns that connect $N=2$ SCFTs in four dimensions to lower-dimensional conformal theories, and they provide explicit holographic data for interfaces and black objects in this gauged supergravity. The study advances understanding of how half-maximal five-dimensional gauged supergravity captures cross-dimensional RG flows, interfaces, and black brane thermodynamics in the M-theory context.

Abstract

We study various types of holographic solutions from five-dimensional $N=4$ gauged supergravity coupled to three vector multiplets with $SO(2)\times ISO(3)$ gauge group. This gauged supergravity can be obtained from the maximal gauged supergravity in seven dimensions on a Riemann surface. For a negatively curved Rimann surface $H^2$, the resulting five-dimensional gauged supergravity admits a supersymmetric $N=4$ $AdS_5$ critical point. This $AdS_5$ vacuum is dual to an $N=2$ superconformal field theory (SCFT) arising from M5-branes wrapped on $H^2$. We study holographic RG flow solutions describing deformations of this SCFT by turning on relevant, marginal and irrelevant operators to $N=2$ non-conformal phases in the IR. Solutions describing conformal interfaces between these non-conformal phases and singular boundaries are also given. We finally study a number of supersymmetric $AdS_5$ black string and black hole solutions holographically dual to RG flows across dimensions from the $N=2$ SCFT to two-dimensional SCFTs and superconformal quantum mechanics in the IR. A number of solutions describing black strings and black holes in asymptotically domain wall space-time is also found. All of the solutions can be uplifted to M-theory by a consistent truncation on $H^2\times S^4$.

Figures (10)

• Figure 1: An $N=1$ supersymmetric RG flow from the $N=2$ SCFT dual to the $N=4$$AdS_5$ vacuum to $N=2$ SYM in the IR for $g=2$.
• Figure 2: An example of Janus solutions interpolating between $N=2$ SYM phases with $\ell=1$, $\kappa=-1$ and $g=2$.
• Figure 3: An example of Janus solutions interpolating between $N=2$ SYM and a singularity with $\ell=1$, $\kappa=-1$ and $g=2$.
• Figure 4: An example of Janus solutions interpolating between singularities on both sides with $\ell=1$, $\kappa=-1$ and $g=2$.
• Figure 5: Examples of supersymmetric $AdS_5$ black string solutions. The orange line represents the solution interpolating between $N=4$$AdS_5$ vacuum and $AdS_3\times H^2$ geometry preserving $8$ supercharges. The red (green) line corresponds to a solution interpolating between $AdS_5$ vacuum and $AdS_3\times H^2$ ($AdS_3\times S^2$) preserving $4$ supercharges.