Non-Supersymmetric Membrane Flows from Fake Supergravity and Multi-Trace Deformations

Abstract

We use fake supergravity as a solution generating technique to obtain a continuum of non-supersymmetric asymptotically $Ad{S}_4\times S^7$ domain wall solutions of eleven-dimensional supergravity with non-trivial scalars in the $SL(8,\mathbb{R})/SO(8)$ coset. These solutions are continuously connected to the supersymmetric domain walls describing a uniform sector of the Coulomb branch of the $M2$-brane theory. We also provide a general argument that under certain conditions identifies the fake superpotential with the exact large-N quantum effective potential of the dual theory, describing a marginal multi-trace deformation. This identification strongly motivates further study of fake supergravity as a solution generating method and it allows us to interpret our non-supersymmetric solutions as a family of marginal triple-trace deformations of the Coulomb branch that completely break supersymmetry and to calculate the exact large-N anomalous dimensions of the operators involved. The holographic one- and two-point functions for these solutions are also computed.

45 pages; v2 minor corrections, Section 8 revised, an appendix and references added; v3 expanded discussion of one- and two-point functions. Version to appear in JHEP

References in corpus (3)

• Hidden supersymmetry of domain walls and cosmologies
• AdS/CFT correspondence and Geometry
• Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4

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