New N=2 Supersymmetric Membrane Flow In Eleven-Dimensional Supergravity

Understand

We construct the 11-dimensional lift of the known N=2 supersymmetric RG flow solution in 4-dimensional N=8 gauged supergravity.

• The squashed and stretched 7-dimensional internal metric preserving SU(2) x U(1) x U(1)_R symmetry contains an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein Y^{p, q} space found in 2004.
• The nontrivial r(transverse to the domain wall)-dependence of the AdS_4 supergravity fields makes the Einstein-Maxwell equations consistent not only at the critical points but also along the supersymmetric whole RG flow connecting two critical points.
• With an appropriate 3-form gauge field, we find an exact solution to the 11-dimensional Einstein-Maxwell equations corresponding to the above lift of the SU(2) x U(1) x U(1)_R-invariant RG flow.