Supersymmetric Domain Wall and RG Flow from 4-Dimensional Gauged N=8 Supergravity

TL;DR

This paper investigates supersymmetric domain walls and RG flows in 4D gauged N=8 supergravity, analyzing various sectors and their critical points, and constructing explicit solutions that connect UV and IR fixed points in the dual 3D CFT.

Contribution

It provides a detailed analysis of RG flows and domain-wall solutions in different sectors of gauged N=8 supergravity, including explicit scalar potentials and first-order solutions, extending previous work.

Findings

Identified superpotential eigenvalues related to RG flows.

Constructed explicit first-order BPS domain-wall solutions.

Analyzed stability and structure of critical points in various sectors.

Abstract

By studying various, known extrema of 1) SU(3) sectors, 2) SO(5) sectors and 3) SO(3)xSO(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 UV 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)xSO(3) sectors, we construct the scalar potential(never been written) explicitly and study explicit construction of first-order domain-wall solutions.