Domain wall from gauged d=4, supergravity: part I

Abstract

By studying already known extrema of non-semi-simple Inonu-Wigner contraction CSO(p, q) + and non-compact SO(p, q) + (p + q = 8) gauged N = 8 supergravity in 4-dimensions developed by Hull sometime 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. IntroductionOne of the interesting issues in recent research is the domain wall(DW)/quantum field theory(QFT) correspondence initiated by [1] between supergravity, in the near horizon region of the corresponding supergravity brane solution, compactified on domain wall spacetimes that are locally isometric to Anti-de Sitter(AdS) space but different from it globally and quantum(nonconformal) field theories describing the internal dynamics of branes and living on the boundary of such spacetimes. DW/QFT correspondence was motivated by the fact that the AdS metric in horospherical coordinates is a special case of the domain wall metric [2,3]. Rsymmetry of the supersymmetric QFT on the boundary of domain worldvolume should match with the gauge group of the corresponding gauged supergravity. Compact gaugings are not the only ones for extended supergravities but there exists a rich structure of non-compact and nonsemi-simple gaugings (Note that the unitarity property is preserved since in all extrema of scalar potential, non-compact gauge symmetry is reduced to some residual compact subgroup). Such a theory plays a fundamental role in the description of the DW/QFT correspondence as the maximally compact gauged supergravity has played in the AdS/conformal field theory(CFT) duality [4,5,6] that is a correspondence between certain compact gauged supergravities and certain conformal field theories. It would be interesting to identify the appropriate non-compact and non-semi-simple gauged supergravities corresponding to each choice of brane configuration.One of the que...

Holographic RG flows on curved manifolds and the F-theorem

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N $$ \mathcal{N} $$ =2 supersymmetric Janus solutions and flows: from gauged supergravity to M theory

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