Holographic N=1 Supersymmetric Membrane Flows

Abstract

The M-theory lift of N=2 SU(3) x U(1)_R-invariant RG flow via a combinatorical use of the 4-dimensional flow and 11-dimensional Einstein-Maxwell equations was found previously. By taking the three internal coordinates differently and preserving only SU(3) symmetry from the CP^2 space, we find a new 11-dimensional solution of N=1 SU(3)-invariant RG flow interpolating from N=8 SO(8)-invariant UV fixed point to N=2 SU(3) x U(1)_R-invariant IR fixed point in 4-dimensions. We describe how the corresponding 3-dimensional N=1 superconformal Chern-Simons matter theory deforms. By replacing the above CP^2 space with the Einstein-Kahler 2-fold, we also find out new 11-dimensional solution of N=1 SU(2) x U(1)-invariant RG flow connecting above two fixed points in 4-dimensions.