Towards an N=1SU(3)-invariant supersymmetric membrane flow in eleven-dimensional supergravity

The M-theory lift of N=1G2-invariant RG flow via a combinatoric use of the 4-dimensional RG flow and 11-dimensional Einstein-Maxwell equations was found some time ago. The 11-dimensional metric, a warped product of an asymptotically AdS ₄ space with a squashed and stretched 7-sphere, for SU(3)-invariance was found before. In this paper, by choosing the 4-dimensional internal space as CP ² space, we discover an exact solution of N=1G2-invariant flow to the 11-dimensional field equations. By an appropriate coordinate transformation on the three internal coordinates, we also find an 11-dimensional solution of N=1G2-invariant flow interpolating from N=8SO(8)-invariant UV fixed point to N=1G2-invariant IR fixed point. In particular, the 11-dimensional metric and 4-forms at the N=1G2 fixed point for the second solution will provide some hints for the 11-dimensional lift of whole N=1SU(3) RG flow connecting this N=1G2 fixed point to N=2SU(3)×U(1)R fixed point in 4-dimensions.