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7D (non-)susy vacua & DWs from dynamical open strings

Valentina Bevilacqua, Giuseppe Dibitetto, Giuseppe Sudano

Abstract

Warped compactifications of massive type IIA supergravity on a 3-sphere with spacetime-filling O6/D6 sources are known to admit a half-maximal gauged supergravity description in 7D. We study the effect of introducing open string degrees of freedom (scalars and fluxes) in such dimensional reductions, associated with the spacetime-filling sources. From the 7D supergravity point of view, this can be realized by coupling the gravity multiplet with extra vector multiplets and adding new components to the embedding tensor describing the gauging. The scalar potential of the underlying theory exhibits novel AdS7 vacuum solutions, with and without supersymmetry. Finally, we explore the net of domain wall solutions interpolating between the different pairs of vacua, and present analytical as well as numerical solutions.

7D (non-)susy vacua & DWs from dynamical open strings

Abstract

Warped compactifications of massive type IIA supergravity on a 3-sphere with spacetime-filling O6/D6 sources are known to admit a half-maximal gauged supergravity description in 7D. We study the effect of introducing open string degrees of freedom (scalars and fluxes) in such dimensional reductions, associated with the spacetime-filling sources. From the 7D supergravity point of view, this can be realized by coupling the gravity multiplet with extra vector multiplets and adding new components to the embedding tensor describing the gauging. The scalar potential of the underlying theory exhibits novel AdS7 vacuum solutions, with and without supersymmetry. Finally, we explore the net of domain wall solutions interpolating between the different pairs of vacua, and present analytical as well as numerical solutions.
Paper Structure (27 sections, 1 theorem, 176 equations, 11 figures, 8 tables)

This paper contains 27 sections, 1 theorem, 176 equations, 11 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Warped compactifications of massive IIA supergravity
  3. D=7 half-maximal supergravity with vector multiplets
  4. Coupling to 3 vector multiplets
  5. Coupling to 3 + N vector multiplets
  6. Fermionic shift matrices
  7. Coupling to N=3 extra vector multiplets and SO(3) truncation
  8. Analysis of the vacuum structure
  9. Solutions in the origin
  10. Going out of the origin
  11. From flux space to field space
  12. Supergravity action and equations of motion in 10 dimensions
  13. Bulk action
  14. Non-Abelian brane actions
  15. Modified equations of motion
  16. ...and 12 more sections

Key Result

Theorem 1

Consider a theory of Einstein gravity in D dimensions coupled to a set of scalar fields, and assume that its scalar potential $V$ admits some perturbatively stable AdS critical points $\phi_0= \{\phi^I_0\}$. If there exists a globally defined function $f$ such that then any other point in $\mathcal{M}_{\textup{scalar}}$ has higher energy than $\phi_0$ and hence $\phi_0$ is stable against non-pert

Figures (11)

  • Figure 1: Profile of the scalar potential defined by \ref{['eq:7d_fixed_fluxes']}, with its critical points tabulated in \ref{['Tab:7d_Solutions_FixedFluxes']}. The plot is in the plane $T = (\frac{2}{3})^{\frac{1}{2}\,(1 - Y)}$.
  • Figure 2: Profile of the $\mathrm{SO}(3)$-invariant scalar fields along the supersymmetric domain wall interpolating between the two supersymmetric AdS vacua $\mathbf{1'}$ and $\mathbf{1}$ of the scalar potential.
  • Figure 3: Profile of the scalar potential defined by \ref{['eq:7d_fixed_fluxes']}, with its critical points tabulated in \ref{['Tab:7d_Solutions_FixedFluxes']} and the fake superpotentials $f^{\mathbf{1'} a}$, $f^{\mathbf{1'} b}$ computed by solving \ref{['eq:DW_fake_susy']} around $\mathbf{1'}$. The plot is in the plane $T = (\frac{2}{3})^{\frac{1}{2}\,(1 - Y)}$, and we have fixed $q=16$.
  • Figure 4: Profile of the scalar potential defined by \ref{['eq:7d_fixed_fluxes']}, with its critical points tabulated in \ref{['Tab:7d_Solutions_FixedFluxes']} and the fake superpotentials $f^{\mathbf{3'} a}$, $f^{\mathbf{3'} b}$ computed by solving \ref{['eq:DW_fake_susy']} around $\mathbf{3'}$. The plot is in the plane $T = (\frac{2}{3})^{\frac{1}{2}\,(1 - Y)}$, and we have fixed $q=16$.
  • Figure 5: Profile of the scalar potential defined by \ref{['eq:7d_fixed_fluxes']}, with its critical points tabulated in \ref{['Tab:7d_Solutions_FixedFluxes']} and the fake superpotentials $f^{\mathbf{1} a}$, $f^{\mathbf{1} b}$ computed by solving \ref{['eq:DW_fake_susy']} around $\mathbf{1}$. The plot is in the plane $T = (\frac{2}{3})^{\frac{1}{2}\,(1 - Y)}$, and we have fixed $q=16$.
  • ...and 6 more figures

Theorems & Definitions (1)

  • Theorem : Positive energy theorem