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Fake Supergravity and Domain Wall Stability

D. Z. Freedman, C. Nunez, M. Schnabl, K. Skenderis

TL;DR

The paper develops a generalized, non-supersymmetric stability framework for domain-wall solutions (fake supergravity) and extends it to AdS_d-sliced geometries using an su(2) matrix superpotential. It demonstrates non-perturbative stability for the Gutperle-Janus solution and its deformations, and provides a constructive approach to stability with multiple scalars via a Boucher-style composite superpotential. A concrete explicit construction of fake Killing spinors and the corresponding W for Janus solidify the stability arguments, while a simple linear-dilaton solution serves as a useful byproduct and consistency check. Together, these results bolster the non-perturbative stability of non-supersymmetric holographic domain walls in Type IIB and related theories, with implications for AdS/CFT and brane-world scenarios.

Abstract

We review the generalized Witten-Nester spinor stability argument for flat domain wall solutions of gravitational theories. Neither the field theory nor the solution need be supersymmetric. Nor is the space-time dimension restricted. We develop the non-trivial extension required for AdS-sliced domain walls and apply this to show that the recently proposed "Janus" solution of Type IIB supergravity is stable non-perturbatively for a broad class of deformations. Generalizations of this solution to arbitrary dimension and a simple curious linear dilaton solution of Type IIB supergravity are byproducts of this work.

Fake Supergravity and Domain Wall Stability

TL;DR

The paper develops a generalized, non-supersymmetric stability framework for domain-wall solutions (fake supergravity) and extends it to AdS_d-sliced geometries using an su(2) matrix superpotential. It demonstrates non-perturbative stability for the Gutperle-Janus solution and its deformations, and provides a constructive approach to stability with multiple scalars via a Boucher-style composite superpotential. A concrete explicit construction of fake Killing spinors and the corresponding W for Janus solidify the stability arguments, while a simple linear-dilaton solution serves as a useful byproduct and consistency check. Together, these results bolster the non-perturbative stability of non-supersymmetric holographic domain walls in Type IIB and related theories, with implications for AdS/CFT and brane-world scenarios.

Abstract

We review the generalized Witten-Nester spinor stability argument for flat domain wall solutions of gravitational theories. Neither the field theory nor the solution need be supersymmetric. Nor is the space-time dimension restricted. We develop the non-trivial extension required for AdS-sliced domain walls and apply this to show that the recently proposed "Janus" solution of Type IIB supergravity is stable non-perturbatively for a broad class of deformations. Generalizations of this solution to arbitrary dimension and a simple curious linear dilaton solution of Type IIB supergravity are byproducts of this work.

Paper Structure

This paper contains 19 sections, 132 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Domain Walls: Basics and Examples
  3. Flat domain walls.
  4. $AdS_d$-sliced domain walls.
  5. Janus solutions.
  6. Stability of flat domain walls
  7. The Witten-Nester energy and positivity
  8. $E_{WN}$ and conserved charges
  9. Stability of $AdS_d$ domain walls
  10. Killing spinor consistency conditions and the new flow equations.
  11. Explicit Killing spinors.
  12. ${\bf W}(\phi)$ for the Janus solution.
  13. $E_{WN}$ for deformations of the Janus solution.
  14. Stability with additional scalar fields.
  15. A curious linear dilaton solution
  16. ...and 4 more sections

Figures (3)

  • Figure 1: (a) Conformal picture of a constant time slice of the Janusian geometry. The boundary is indicated by the bold arcs. (b) Top view of the same picture. The coordinate $\lambda$ ranges from $0$ at the equator to $\pi/2$ at the north pole. The dashed line indicates the "contour" used to evaluate $E_{WN}$ in Sec. 4.
  • Figure 2: Plot of the magnitude $w(\phi)$ for $d=4$, $L=1$ and $b=0.1$.
  • Figure 3: Plot of the phase $\theta(\phi)$ for $d=4$ and $b=0.1$.