New N=2 supersymmetric membrane flow in eleven-dimensional supergravity

We construct the 11-dimensional lift of the known = 2 supersymmetric RG flow solution in 4-dimensional = 8 gauged supergravity. The squashed and stretched 7-dimensional internal metric preserving SU(2) × U(1) × 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) × U(1) × U(1) _R-invariant RG flow. The particular limits of this solution give rise to the previous solutions with SU(3) × U(1) _R or SU(2) × SU(2) × U(1) _R.