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

TL;DR

This paper constructs a family of non-supersymmetric domain wall solutions in eleven-dimensional supergravity using fake supergravity, interprets them as multi-trace deformations of the Coulomb branch, and computes their holographic correlators.

Contribution

It demonstrates the use of fake supergravity to generate non-supersymmetric solutions and links the fake superpotential to the quantum effective potential of the dual theory.

Findings

Identified fake superpotential with the large-N effective potential.

Constructed non-supersymmetric solutions connected to Coulomb branch.

Computed holographic one- and two-point functions.

Abstract

We use fake supergravity as a solution generating technique to obtain a continuum of non-supersymmetric asymptotically $AdS_4\times S^7$ 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.