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

By analyzing SU(3) x U(1) invariant stationary point, studied earlier by Nicolai and Warner, of gauged N = 8 supergravity, we find that the deformation of S-7 gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N = 8, SO(8) invariant UV fixed paint to N = 2, SU(3) x U(1) invariant IR axed point. By explicitly constructing 28-beins u, v fields, that are an element of fundamental 56-dimensional representation of E-7, in terms of scalar and pseudo-scalar fields of gauged N = 8 supergravity, we get A(1), A(2) tensors. Then we identify one of the eigenvalues of A(1) tensor with superpotential of de Wit-Nicolai scaler potential and discuss four-dimensional supergravity description of renormalization group now, 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. (C) 2001 Elsevier Science B.V. All rights reserved.