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Gravitating Fluxbranes

P. M. Saffin

TL;DR

Gravitating Fluxbranes studies the gravity-induced self-consistency of homogeneous $n$-form backgrounds in $D$ dimensions, producing fluxbranes with worldvolume dimension $D-n-1$ and exploring dilaton couplings. The authors recast the field equations into a two-variable dynamical system via Misner variables, enabling a set of exact fluxbrane solutions for various transverse geometries and including a dilaton extension. Key results include explicit Melvin-like fluxbranes, AdS/Minkowski-type configurations, and a second extension with a positively curved transverse space, all visualized with embedding diagrams; many cores are singular while some asymptotics are regular. The work interprets fluxbranes as brane–antibrane systems at infinite separation, discusses stability and decay channels, and connects to known higher-dimensional constructions and possible instanton decay processes.

Abstract

We consider the effect that gravity has when one tries to set up a constant background form field. We find that in analogy with the Melvin solution, where magnetic field lines self-gravitate to form a flux-tube, the self-gravity of the form field creates fluxbranes. Several exact solutions are found corresponding to different transverse spaces and world-volumes, a dilaton coupling is also considered.

Gravitating Fluxbranes

TL;DR

Gravitating Fluxbranes studies the gravity-induced self-consistency of homogeneous -form backgrounds in dimensions, producing fluxbranes with worldvolume dimension and exploring dilaton couplings. The authors recast the field equations into a two-variable dynamical system via Misner variables, enabling a set of exact fluxbrane solutions for various transverse geometries and including a dilaton extension. Key results include explicit Melvin-like fluxbranes, AdS/Minkowski-type configurations, and a second extension with a positively curved transverse space, all visualized with embedding diagrams; many cores are singular while some asymptotics are regular. The work interprets fluxbranes as brane–antibrane systems at infinite separation, discusses stability and decay channels, and connects to known higher-dimensional constructions and possible instanton decay processes.

Abstract

We consider the effect that gravity has when one tries to set up a constant background form field. We find that in analogy with the Melvin solution, where magnetic field lines self-gravitate to form a flux-tube, the self-gravity of the form field creates fluxbranes. Several exact solutions are found corresponding to different transverse spaces and world-volumes, a dilaton coupling is also considered.

Paper Structure

This paper contains 15 sections, 39 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Melvin solution and its generalization
  3. Equations of motion
  4. Curvature equations
  5. Source equations
  6. Dynamical system
  7. Melvin solutions
  8. First extension, $\Lambda_{\rm (L)}\neq 0$, $\Lambda_{\rm (E)}=0$, $\rm m\geq1$
  9. $\Lambda_{\rm (L)}>0$, $\Lambda_{\rm (E)}=0$, $m>1$
  10. $\Lambda_{\rm (L)}<0$, $\Lambda_{\rm (E)}=0$, $m>1$
  11. Second extension, $\Lambda_{\rm (L)}=0$, $\Lambda_{\rm (E)}>0$, $m\geq 1$
  12. Embedding diagram
  13. Dilatonic fluxbranes
  14. Discussion
  15. Acknowledgements

Figures (5)

  • Figure 1: Solutions for the Ricci flat world-volume and Euclidean manifold. The core of the fluxbrane, $\xi\rightarrow -\infty$, is at $A,c\rightarrow -\infty$.
  • Figure 2: Solutions for the positively curved world-volume and Ricci flat Euclidean manifold. The core of the fluxbrane, $\xi\rightarrow -\infty$, takes the values $A,c\rightarrow -\infty$.
  • Figure 3: Solutions for the negatively curved world-volume and Ricci flat Euclidean manifold. The core of the fluxbrane, $\xi\rightarrow -\infty$, takes the values $A,c\rightarrow -\infty$. The fact that $A,c$ turn around and diverge back to $-\infty$ is the reason why there is a singularity at finite proper distance from the core.
  • Figure 4: Solutions for the Ricci flat world-volume and positively curved Euclidean manifold, eg. a round metric. The core of the fluxbrane, $\xi\rightarrow -\infty$, takes the values $A,c\rightarrow -\infty$.
  • Figure 5: Here we show the embedding diagrams for the various solutions. They describe how the volume of the Euclidean manifold, $\exp(c(\xi))$, varies as we move away from the core. To compare between cases we plot the volume as a function of proper distance.