Superconformal interfaces from 5D N=4 gauged supergravity

TL;DR

The paper addresses how to realize conformal interfaces in 4D SCFTs holographically by exploring supersymmetric Janus solutions within five-dimensional $N=4$ gauged supergravity. It develops BPS equations for AdS$_4$-sliced domain walls in two setups: (i) a truncation of $SO(2)\times SO(3)\times SO(3)$ to $SO(2)\times SO(3)\times SO(3)$ with two $N=4$ vacua, and (ii) the full $SO(2)_D\times SO(3)\times SO(3)$ theory with four $AdS_5$ vacua (two $N=4$, two $N=2$). The authors construct and numerically analyze a large class of Janus and multi-Janus solutions interpolating among these vacua, including RG-flow interfaces, and provide an interpretation in terms of relevant/irrelevant operator deformations in the dual SCFTs, with detailed operator-dimension mappings near the fixed points. Although no higher-dimensional origin is currently known for these specific gaugings, the results offer a robust framework for studying interfaced holographic CFTs and motivate future uplifts to string/M-theory and identifications of dual $N=1$ and $N=2$ SCFTs.

Abstract

We find a large class of new supersymmetric Janus solutions from five-dimensional $N=4$ gauged supergravity coupled to five vector multiplets with $SO(2)_D\times SO(3)\times SO(3)$ gauge group. The gauged supergravity admits four supersymmetric $AdS_5$ vacua, two $N=4$ with $SO(2)_D\times SO(3)\times SO(3)$ and $SO(2)_D\times SO(3)_{\textrm{diag}}$ symmetric $AdS_5$ vacua and two $N=2$ with $SO(2)_{\textrm{diag}}\times SO(3)$ and $SO(2)_{\textrm{diag}}$ symmetric ones. In a truncation to three vector multiplets, the gauge group is given by $SO(2)\times SO(3)\times SO(3)$, and the resulting gauged supergravity admits only two $N=4$ supersymmetric $AdS_5$ vacua with $SO(2)\times SO(3)\times SO(3)$ and $SO(2)\times SO(3)_{\textrm{diag}}$ residual symmetries. By considering the $SO(2)_{\textrm{diag}}$ invariant sector within this truncation, we find a number of supersymetric Janus interfaces between the two $N=4$ vacua on both sides as well as an RG-flow interface between $SO(2)\times SO(3)\times SO(3)$ and $SO(2)\times SO(3)_{\textrm{diag}}$ symmetric vacua on each side. By repeating the analysis in the full $SO(2)_D\times SO(3)\times SO(3)$ gauged supergravity, we find Janus solutions interpolating between the aforementioned four supersymmetric $AdS_5$ vacua as well as examples of multi-Janus interfaces between these vacua.

Figures (6)

• Figure 1: Examples of Janus solutions interpolating between $N=4$$AdS_5$ critical point I (red) and between $N=4$$AdS_5$ critical point II (green). The blue line corresponds to a solution interpolating between critical point I that flows close to critical point II. In these solutions, we have chosen the numerical values of $\ell=1$, $\kappa=-1$, $h_1=2$, $g_1=-\sqrt{2}$ and $h_2=4$.
• Figure 2: An example of RG-flow interfaces interpolating between $N=4$$AdS_5$ vacua given by critical points I and II with $\ell=1$, $\kappa=-1$, $h_1=2$, $g_1=-\sqrt{2}$ and $h_2=4$.
• Figure 3: Examples of supersymmetric Janus solutions interpolating between $AdS_5$ vacua given by critical point II (red), III (green) and IV (blue).
• Figure 4: An example of multi-Janus interfaces interpolating between $AdS_5$ vacua given by critical points I, II, III and IV. This solution describes three conformal interfaces, two interfaces between critical point I on the right and left of the origin and one interface between critical point IV at the origin.
• Figure 5: An example of multi-Janus interfaces interpolating between $AdS_5$ vacua given by critical points I, II, III and IV. This solution describes five conformal interfaces, four interfaces between critical point I on the right and left of the origin and one interface between critical point III at the origin.