Holographic N = 1 supersymmetric membrane flows

The M-theory lift of N = 2 SU(3) × U(1)_R -invariant RG flow via a combinatorical use of the four-dimensional flow and 11-dimensional Einstein- Maxwell equations was found previously. By taking the three internal coordinates differently and preserving only the SU(3) symmetry from the CP ² space, we find a new 11-dimensional solution of the N = 1 SU(3)-invariant RG flow interpolating from the N = 8 SO(8)-invariant UV fixed point to the N = 2 SU(3) × U(1)_R-invariant IR fixed point in four dimensions. We describe how the corresponding three-dimensional N = 1 superconformal Chern-Simons matter theory deforms. By replacing the above CP² space with the Einstein-Kahler twofold, we also find out a new 11-dimensional solution of the N = 1 SU(2)×U(1)-invariant RG flow connecting the above two fixed points in four dimensions.