Three-dimensional SCFTs, supersymmetric domain wall and renormalization group flow

By analyzing SU(3)×U(1) invariant stationary point, studied earlier by Nicolai and Warner, of gauged N=8 supergravity, we find that the deformation of S⁷ gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N=8, SO(8) invariant UV fixed point to N=2, SU(3)×U(1) invariant IR fixed point. By explicitly constructing 28-beins u,v fields, that are an element of fundamental 56-dimensional representation of E₇, in terms of scalar and pseudo-scalar fields of gauged N=8 supergravity, we get A₁,A₂ tensors. Then we identify one of the eigenvalues of A₁ tensor with "superpotential" of de Wit-Nicolai scalar potential and discuss four-dimensional supergravity description of renormalization group flow, i.e., the BPS domain wall solutions which are equivalent to vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving bosonic background of gauged N=8 supergravity. A numerical analysis of the steepest descent equations interpolating two critical points is given.