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

TL;DR

This paper constructs an 11-dimensional supergravity solution representing a supersymmetric membrane flow, extending known 4D solutions and connecting different symmetry-preserving limits, with implications for M-theory and holography.

Contribution

It provides the explicit 11D lift of a known N=2 supersymmetric RG flow in 4D supergravity, including a new exact solution with a nontrivial internal geometry.

Findings

Exact 11D supergravity solution for N=2 supersymmetric flow.

The solution interpolates between known symmetric limits.

The internal geometry involves Einstein-Kahler and Sasaki-Einstein structures.

Abstract

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. The particular limits of this solution give rise to the previous solutions with SU(3) x U(1)_R or SU(2) x SU(2) x U(1)_R.