Supersymmetric domain wall and RG flow from 4-dimensional gauged N=8 supergravity

By studying various, known extreme of 1) SU(3) sectors, 2) SO(5) sectors and 3) SO(3) x SO(3) sectors of gauged N = 8 supergravity in four dimensions, one finds that the deformation of seven sphere S-7 gives rise to non-trivial renormalization group (RG) flow in three-dimensional boundary conformal field theory from W fixed point to IR fixed point. For SU(3) sectors, this leads to four-parameter subspace of the supergravity scalar-gravity action and we identify one of the eigenvalues of A(1) tensor of the theory with a superpotential of scalar potential that governs RG flows on this subspace. We analyze some of the structure of the superpotential and discuss first-order BPS domain-wall solutions, using some algebraic relations between superpotential and derivatives of it with respect to fields, that determine a (super)symmetric kink solution in four-dimensional N = 8 supergravity, which generalizes all the previous considerations. The BPS domain-wall solutions are equivalent to vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving bosonic background of gauged N = 8 supergravity. For SO(5) sectors, there exist only nontrivial nonsupersymmetric critical points that are unstable and included in SU(3) sectors. For SO(3) x SO(3) sectors, we construct the scalar potential (never been written) explicitly and study explicit construction of first-order domain-wall solutions. (C) 2001 Published by Elsevier Science B.V.