Abstract
We study supersymmetric solutions within seven-dimensional $N=2$ gauged supergravity coupled to three vector multiplets in seven dimensions. The gauged supergravity contains six vector fields that gauge the $SO(4)\sim SO(3)\times SO(3)$ symmetry and admits two $N=2$ supersymmetric $AdS_7$ vacua with $SO(4)$ and $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)$ symmetries. We consider solutions interpolating between two asymptotically locally $AdS_7$ geometries in the presence of a three-form field. For a particular value of the two $SO(3)$ gauge coupling constants, the $SO(3)_{\textrm{diag}}$ supersymmetric $AdS_7$ vacuum does not exist, but the solutions can be uplifted to eleven dimensions by a known reduction ansatz. We also study solutions of this type and their embedding in M-theory. We further extend these solutions to include the $SO(3)_{\textrm{diag}}$ gauge fields and argue that, in general, this generalization does not lead to supersymmetric solutions.
Highlights
Over the past 20 years, the AdS=CFT correspondence has been widely tested and confirmed by a large number of interesting results
One of the interesting cases is AdS7=CFT6 correspondence which has been argued to describe the dynamics of M5 branes in M theory since the first proposal of the correspondence in Ref. [1]
AdS7=CFT6 correspondence can be efficiently investigated by using gauged supergravities in seven dimensions
Summary
Over the past 20 years, the AdS=CFT correspondence has been widely tested and confirmed by a large number of interesting results. We are interested in similar solutions in N 1⁄4 2 gauged supergravity coupled to three vector multiplets with the SOð4Þ ∼ SOð3Þ × SOð3Þ gauge group In this case, the maximally supersymmetric AdS7 vacuum is dual to an N 1⁄4 ð1; 0Þ SCFT with flavor symmetry SOð3Þ. Apart from the gauging, there is a massive deformation given by adding a topological mass term to the three-form field Cμνρ. This additional deformation is crucial for the gauged supergravity to admit AdS7 vacua. Holographic renormalization group flow solutions interpolating between these two critical points and flows to nonconformal field theories have already been given in Ref. Holographic renormalization group flow solutions interpolating between these two critical points and flows to nonconformal field theories have already been given in Ref. [19]
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