Domain wall from gauged d=4, [formula omitted] supergravity: part I

Abstract

By studying already known extrema of nonsemisimple Inonu–Wigner contraction CSO( p, q) + and noncompact SO( p, q) +( p+ q=8) gauged N=8 supergravity in 4 dimensions developed by Hull some time ago, one expects there exists nontrivial flow in the 3-dimensional boundary field theory. We find that these gaugings provide first-order domain-wall solutions from direct extremization of energy density. We also consider the most general CSO( p, q, r) + with p+ q+ r=8 gauging of N=8 supergravity by two successive SL(8, R) transformations of the de Wit–Nicolai theory, that is, compact SO(8) gauged supergravity. The theory found earlier has local SU(8)× CSO( p, q, r) + gauge symmetry as well as local N=8 supersymmetry. The gauge group CSO( p, q, r) + is spontaneously reduced to its maximal compact subgroup SO( p) +× SO( q) +× U(1) + r( r−1)/2 . The T-tensor we obtain describes a two-parameter family of gauged N=8 supergravity from which one can construct A 1 and A 2 tensors. The effective nontrivial scalar potential can be written as the difference of positive definite terms. We examine the scalar potential for critical points at which the expectation value of the scalar field is SO( p) +× SO( q) +× SO( r) + invariant. It turns out that there is no new extra critical point. However, we do have flow equations and domain-wall solutions for the scalar fields are the gradient flow equations of the superpotential that is one of the eigenvalues of A 1 tensor.