Supersymmetric RG flows and Janus from type II orbifold compactification

We study holographic RG flow solutions within four-dimensional $N=4$ gauged supergravity obtained from type IIA and IIB string theories compactified on $T^6/\mathbb{Z}_2\times \mathbb{Z}_2$ orbifold with gauge, geometric and non-geometric fluxes. In type IIB non-geometric compactifications, the resulting gauged supergravity has $ISO(3)\times ISO(3)$ gauge group and admits an $N=4$ $AdS_4$ vacuum dual to an $N=4$ superconformal field theory (SCFT) in three dimensions. We study various supersymmetric RG flows from this $N=4$ SCFT to $N=4$ and $N=1$ non-conformal field theories in the IR. The flows preserving $N=4$ supersymmetry are driven by relevant operators of dimensions $\Delta =1,2$ or alternatively by one of these relevant operators, dual to the dilaton, and irrelevant operators of dimensions $\Delta=4$ while the $N=1$ flows in addition involve marginal deformations. Most of the flows can be obtained analytically. We also give examples of supersymmetric Janus solutions preserving $N=4$ and $N=1$ supersymmetries. These solutions should describe two-dimensional conformal defects within the dual $N=4$ SCFT. Geometric compactifications of type IIA theory give rise to $N=4$ gauged supergravity with $ISO(3)\ltimes U(1)^6$ gauge group. In this case, the resulting gauged supergravity admits an $N=1$ $AdS_4$ vacuum. We also numerically study possible $N=1$ RG flows to non-conformal field theories in this case.Comment: 32 pages, 5 figures, typos corrected and references adde

Holographic RG flows in N=4 SCFTs from half-maximal gauged supergravity

We study four-dimensional $N=4$ gauged supergravity coupled to six vector multiplets with semisimple gauge groups $SO(4)\times SO(4)$, $SO(3,1)\times SO(3,1)$ and $SO(4)\times SO(3,1)$. All of these gauge groups are dyonically embedded in the global symmetry group $SO(6,6)$ via its maximal subgroup $SO(3,3)\times SO(3,3)$. For $SO(4)\times SO(4)$ gauge group, there are four $N=4$ supersymmetric $AdS_4$ vacua with $SO(4)\times SO(4)$, $SO(4)\times SO(3)$, $SO(3)\times SO(4)$ and $SO(3)\times SO(3)$ symmetries, respectively. These $AdS_4$ vacua correspond to $N=4$ SCFTs in three dimensions with $SO(4)$ R-symmetry and different flavor symmetries. We explicitly compute the full scalar mass spectra at all these vacua. Holographic RG flows interpolating between these conformal fixed points are also given. The solutions describe supersymmetric deformations of $N=4$ SCFTs by relevant operators of dimensions $\Delta=1,2$. A number of these solutions can be found analytically although some of them can only be obtained numerically. These results provide a rich and novel class of $N=4$ fixed points in three-dimensional Chern-Simons-Matter theories and possible RG flows between them in the framework of $N=4$ gauged supergravity in four dimensions. Similar studies are carried out for non-compact gauge groups, but the $SO(4)\times SO(4)$ gauge group exhibits a much richer structure.Comment: 31 pages, 4 figures, typos corrected and references adde