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

Abstract

By studying various, known extrema of 1) SU(3) sectors, 2) SO(5) sectors and 3) SO(3) × 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 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) × SO(3) sectors, we construct the scalar potential(never been written) explicitly and study explicit construction of first-order domain-wall solutions. de Wit-Nicolai Potentialde Wit and Nicolai [16,17] constructed a four-dimensional supergravity theory by gauging the SO(8) subgroup of E 7 in the global E 7 × local SU(8) supergravity of Cremmer and Julia [18] by introducing the appropriate couplings by hand and then constructing the supersymmetry model by Noether procedure. In common with Cremmer-Julia theory, this theory contains selfinteraction of a single massless N = 8 supermultiplet of spins (2, 3/2, 1, 1/2, 0 + , 0 − ) but with local SO(8) × local SU(8) invariance. There is a new parameter, the SO(8) gauge coupling constant g besides the gravitational constant. In order to preserve the N = 8 supersymmetry, they modified the Cremmer-Julia Lagrangian and transformation rules by other g-dependent terms. In particular, there was a non-trivial effective potential for the scalars that is proportional to the square of the SO(8) gauge coupling. It is well known [19] that the 70 real, physical scalars of N = 8 supergravity parametrize the coset space E 7 /SU(8)(even though E 7 symmetry is broken in the gauged theory) since 63 fields(133 − 63 = 70) may be gauged away by an SU (8) rotation(maximal compact subgroup of E 7 ) and can be described by an element V(x) of the

Holographic RG flow in a new SO(3) × SO(3) sector of ω-deformed SO(8) gauged N = 8 $$ \mathcal{N}=8 $$ supergravity

“…Cases that have been studied involve retaining the subset of scalar fields invariant under an SO(7), G 2 , SU(3) or SO(3) × SO(3) subgroup [3,[5][6][7][8][9], or else the seven scalars parameterising the diagonal elements of the SL(8, R)/SO(8) coset associated with the 35 self-dual scalars [10]. These various truncations are parallel to the consistent scalar-field truncations performed for the the original de Wit-Nicolai theory [11][12][13][14][15][16][17][18][19]. Consistent truncations retaining U(1) gauge fields have also been considered, giving rise to an ω-deformed version of the ST U supergravity [20], and a one-parameter extension [21] of an Einstein-Maxwell-scalar system [22] previously obtained via a reduction from eleven dimensions on a seven-dimensional Sasaki-Einstein manifold.…”

“…The action (including the Gibbons-Hawking term) evaluated on the domain-wall ansatz is given by 15) and this is clearly extremised by the solutions of (2.14). (Here we adopt the same notation as [13].) Using γ 2 ǫ 8 = (ǫ 8 ) * , and 17) where ε 1 and ε 1 are two real constants.…”

Supersymmetric RG flows and Janus from type II orbifold compactification

“…It should also be noted that there are two scalars which are singlet under (3)] diag as can be seen by taking the tensor product of the representation 6 in (24) giving rise to two singlets (1, 1) of SO (3)×SO (3). These two singlets correspond to ϕ 1 and ϕ 2 .…”

“…Most of the previously studied holographic RG flows have been found within the maximal N = 8 gauged supergravities [2][3][4][5][6][7][8][9]. Many of these solutions describe various deformations of the N = 8 SCFTs arising from M2-brane world-volume proposed in [10,11].…”

“…They correspond to N = 4 and N = 1 SCFTs in three dimensions with global symmetries SO(3) × SO (3) and SO (3), respectively. We will look for possible supersymmetric deformations within these two SCFTs in the form of RG flows to non-conformal phases preserving some amount of supersymmetry.…”