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N=4 "Fake" Supergravity

Marco Zagermann

TL;DR

The paper extends the fake supergravity formalism to $5D$, $oldsymbol{N}=4$ gauged supergravity, showing that the BPS-domain-wall dynamics along the flow can be captured by a generalized fake-supergravity description with a matrix gravitino shift $oldsymbol{W}$ in $oldsymbol{usp}(4)$. It proves that walls sourced solely by the supergravity scalar are necessarily flat and that purely Abelian or purely semisimple gaugings cannot produce curved walls, with flat walls exhibiting runaway behavior in the dilaton-like direction. When multiple scalar sectors are active, an adapted flow can often be described by an effective one-field fake-supergravity system, though the presence of $oldsymbol{usp}(4)$ structure introduces novel features absent in the $N=2$ case. The results suggest a potential universality of the fake-supergravity description across gauged supergravity theories and offer practical tools for analyzing holographic RG flows and domain-wall backgrounds arising in flux compactifications. Overall, the work clarifies how curvature and stability of domain walls are controlled by gauging data and the interplay of fermionic shifts, illuminating a path toward a unified treatment of BPS-domain walls in diverse supergravity theories.

Abstract

We study curved and flat BPS-domain walls in 5D, N=4 gauged supergravity and show that their effective dynamics along the flow is described by a generalized form of "fake supergravity". This generalizes previous work in N=2 supergravity and might hint towards a universal behavior of gauged supergravity theories in supersymmetric domain wall backgrounds. We show that BPS-domain walls in 5D, N=4 supergravity can never be curved if they are supported by the supergravity scalar only. Furthermore, a purely Abelian gauge group or a purely semisimple gauge group can never lead to a curved domain wall, and the flat walls for these gaugings always exhibit a runaway behavior.

N=4 "Fake" Supergravity

TL;DR

The paper extends the fake supergravity formalism to , gauged supergravity, showing that the BPS-domain-wall dynamics along the flow can be captured by a generalized fake-supergravity description with a matrix gravitino shift in . It proves that walls sourced solely by the supergravity scalar are necessarily flat and that purely Abelian or purely semisimple gaugings cannot produce curved walls, with flat walls exhibiting runaway behavior in the dilaton-like direction. When multiple scalar sectors are active, an adapted flow can often be described by an effective one-field fake-supergravity system, though the presence of structure introduces novel features absent in the case. The results suggest a potential universality of the fake-supergravity description across gauged supergravity theories and offer practical tools for analyzing holographic RG flows and domain-wall backgrounds arising in flux compactifications. Overall, the work clarifies how curvature and stability of domain walls are controlled by gauging data and the interplay of fermionic shifts, illuminating a path toward a unified treatment of BPS-domain walls in diverse supergravity theories.

Abstract

We study curved and flat BPS-domain walls in 5D, N=4 gauged supergravity and show that their effective dynamics along the flow is described by a generalized form of "fake supergravity". This generalizes previous work in N=2 supergravity and might hint towards a universal behavior of gauged supergravity theories in supersymmetric domain wall backgrounds. We show that BPS-domain walls in 5D, N=4 supergravity can never be curved if they are supported by the supergravity scalar only. Furthermore, a purely Abelian gauge group or a purely semisimple gauge group can never lead to a curved domain wall, and the flat walls for these gaugings always exhibit a runaway behavior.

Paper Structure

This paper contains 13 sections, 120 equations, 1 figure.

Table of Contents

  1. Introduction
  2. True and fake $5D$, $\mathcal{N}=2$ supergravity
  3. 5D, $\mathcal{N}=2$ gauged supergravity
  4. Curved and flat BPS-domain walls
  5. The relation to ($\mathcal{N}=2$) "fake" supergravity
  6. BPS-domain walls in $\mathcal{N}=4$ fake and true supergravity
  7. Ungauged 5D, $\mathcal{N}=4$ supergravity
  8. 5D, $\mathcal{N}=4$ gauged supergravity
  9. BPS-domain walls
  10. Consistency conditions and domain wall curvature
  11. Special cases
  12. Conclusions
  13. The flatness condition

Figures (1)

  • Figure 1: A given domain wall defines a flow curve (thick arrow) on the scalar manifold $\mathcal{M}_{\rm VS}$. In a), the thin arrows correspond to a generic coordinate system $\varphi^{x}= (\varphi^1,\varphi^2)$. In b), the coordinate system $\varphi^{x}=(\varphi,\varphi^{\hat{x}})$ is adapted to the flow curve, i.e., the flow curve coincides with a coordinate line of $\varphi$ and intersects the coordinate lines $\varphi^{\hat{x}}$ at right angles.