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

Ioannis Papadimitriou

TL;DR

This work develops fake supergravity as a robust tool to generate non-supersymmetric, asymptotically AdS domain walls in M-theory, explicitly connecting four-dimensional membrane flows to eleven-dimensional uplifts on $AdS_4 imes S^7$. It shows that, under suitable conditions, the fake superpotential reproduces the exact large-$N$ quantum effective potential for marginal multi-trace deformations, enabling a precise holographic interpretation as marginal triple-trace deformations of the M2-brane Coulomb branch. The authors compute holographic 1- and 2-point functions, classify the possible non-supersymmetric flows (with analytic results in $D=4$, including a continuum of solutions and an exact $k=6$ case), and analyze the resulting operator dimensions and Ward identities. The results illuminate the role of fake supergravity as a solution-generating technique and provide a concrete holographic framework for marginal multi-trace deformations in highly symmetric flux backgrounds.

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.

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

TL;DR

This work develops fake supergravity as a robust tool to generate non-supersymmetric, asymptotically AdS domain walls in M-theory, explicitly connecting four-dimensional membrane flows to eleven-dimensional uplifts on . It shows that, under suitable conditions, the fake superpotential reproduces the exact large- quantum effective potential for marginal multi-trace deformations, enabling a precise holographic interpretation as marginal triple-trace deformations of the M2-brane Coulomb branch. The authors compute holographic 1- and 2-point functions, classify the possible non-supersymmetric flows (with analytic results in , including a continuum of solutions and an exact case), and analyze the resulting operator dimensions and Ward identities. The results illuminate the role of fake supergravity as a solution-generating technique and provide a concrete holographic framework for marginal multi-trace deformations in highly symmetric flux backgrounds.

Abstract

We use fake supergravity as a solution generating technique to obtain a continuum of non-supersymmetric asymptotically domain wall solutions of eleven-dimensional supergravity with non-trivial scalars in the coset. These solutions are continuously connected to the supersymmetric domain walls describing a uniform sector of the Coulomb branch of the -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.

Paper Structure

This paper contains 17 sections, 191 equations.

Table of Contents

  1. Introduction and summary of results
  2. The $SL(N,\mathbb{R})/SO(N)$ sector of gauged maximal supergravity and its higher-dimensional origin
  3. All asymptotically AdS Poincaré domain walls of the $SL(N,\mathbb{R})/SO(N)$ sector
  4. The non-supersymmetric Poincaré domain walls in $D=4$
  5. Domain walls with a single scalar
  6. Exact closed form solutions
  7. Exact non-supersymmetric membrane flows
  8. Holographic one-point functions
  9. $\Delta=\Delta_+$
  10. $\Delta=\Delta_-$
  11. Holographic two-point functions
  12. The fake superpotential as a quantum effective potential and multi-trace deformations
  13. Triple-trace deformation of the Coulomb branch
  14. Explicit form of the domain wall metric for $W(\phi;\alpha)$, to first order in $\alpha-\alpha_o$ and for general $k$
  15. Uplifting the MTZ black hole to eleven dimensions
  16. ...and 2 more sections