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Dynamical Decay of Brane-Antibrane and Dielectric Brane

Koji Hashimoto

TL;DR

This work analyzes the time-dependent decay of two archetypal unstable brane systems: a parallel Dp–Dpbar pair with separation $l$ and Myers' dielectric branes in a constant RR field. It combines tachyon effective field theory for brane–antibrane annihilation with DBI-based dielectric-brane dynamics and computes explicit decay widths via Euclidean bounce solutions, including funnel- and doughnut-shaped geometries. The brane–antibrane decay proceeds through nucleation of a true-vacuum throat with radius $R_0$ (scaling as $R_0 \sim \frac{p}{2}l$) and rate $\Gamma \sim \exp(-S_E)$, while dielectric-brane decay is governed by funnel-shaped bounces with actions that depend on the RR background $f$ and D0 charge $N_{D0}$. The paper also extends the analysis to scalar-field effects, topological defects, D0–D0bar decay, and nucleation-from-nothing scenarios, offering a concrete, computable bridge between tachyon condensation and nonperturbative brane dynamics with potential relevance to braneworld cosmology and string vacuum structure.

Abstract

Using D-brane effective field theories, we study dynamical decay of unstable brane systems : (i) a parallel brane-antibrane pair with separation l and (ii) a dielectric brane. In particular we give explicitly the decay width of these unstable systems, and describe how the decay proceeds after the tunnel effect. The decay (i) is analysed by the use of a tachyon effective action on the Dp-Dpbar. A pair annihilation starts by nucleation of a bubble of a tachyon domain wall which represents a throat connecting these branes, and the tunneling decay width is found to be proportional to exp(-l^{p+1} T_{Dp}). We study also the decay leaving topological defects corresponding to lower-dimensional branes, which may be relevant for recent inflationary braneworld scenario. As for the decay (ii), first we observe that Dp-branes generically ``curl up'' in a nontrivial RR field strength. Using this viewpoint, we compute the decay width of the dielectric D2-branes by constructing relevant Euclidean bounce solutions in the shape of a funnel. We also give new solutions in doughnut shape which are involved with nucleation of dielectric branes from nothing.

Dynamical Decay of Brane-Antibrane and Dielectric Brane

TL;DR

This work analyzes the time-dependent decay of two archetypal unstable brane systems: a parallel Dp–Dpbar pair with separation and Myers' dielectric branes in a constant RR field. It combines tachyon effective field theory for brane–antibrane annihilation with DBI-based dielectric-brane dynamics and computes explicit decay widths via Euclidean bounce solutions, including funnel- and doughnut-shaped geometries. The brane–antibrane decay proceeds through nucleation of a true-vacuum throat with radius (scaling as ) and rate , while dielectric-brane decay is governed by funnel-shaped bounces with actions that depend on the RR background and D0 charge . The paper also extends the analysis to scalar-field effects, topological defects, D0–D0bar decay, and nucleation-from-nothing scenarios, offering a concrete, computable bridge between tachyon condensation and nonperturbative brane dynamics with potential relevance to braneworld cosmology and string vacuum structure.

Abstract

Using D-brane effective field theories, we study dynamical decay of unstable brane systems : (i) a parallel brane-antibrane pair with separation l and (ii) a dielectric brane. In particular we give explicitly the decay width of these unstable systems, and describe how the decay proceeds after the tunnel effect. The decay (i) is analysed by the use of a tachyon effective action on the Dp-Dpbar. A pair annihilation starts by nucleation of a bubble of a tachyon domain wall which represents a throat connecting these branes, and the tunneling decay width is found to be proportional to exp(-l^{p+1} T_{Dp}). We study also the decay leaving topological defects corresponding to lower-dimensional branes, which may be relevant for recent inflationary braneworld scenario. As for the decay (ii), first we observe that Dp-branes generically ``curl up'' in a nontrivial RR field strength. Using this viewpoint, we compute the decay width of the dielectric D2-branes by constructing relevant Euclidean bounce solutions in the shape of a funnel. We also give new solutions in doughnut shape which are involved with nucleation of dielectric branes from nothing.

Paper Structure

This paper contains 20 sections, 105 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Decay of dielectric brane
  3. Introductory remarks
  4. Curled-up branes and reformulation of dielectric effect
  5. Nucleation and expansion of spherical D$p$-brane
  6. Decay width of dielectric D2-brane
  7. Nucleation of dielectric brane from nothing
  8. Decay of brane-antibrane
  9. Introductory remarks
  10. Naive prospect
  11. Description of brane-antibrane by tachyon field
  12. Decay width of brane-antibrane
  13. Coleman's computation in arbitrary dimension
  14. Application to ours
  15. Inclusion of scalar field
  16. ...and 5 more sections

Figures (17)

  • Figure 1: Potential energy for the spherical D2-brane with the magnetic flux on it. We chose $N_{{\rm D0}}=1$ in the unit ${\alpha'}=1$. The point A is a local minimum which corresponds to the dielectric brane. It decays by quantum tunneling to the larger spherical brane (B).
  • Figure 2: Potential energy with no magnetic flux. There is no local minimum except $R=0$.
  • Figure 3: A curled-up brane in the background constant RR field strength with negative $f$.
  • Figure 4: A curled-up brane with positive $f$.
  • Figure 5: Nucleation of a spherical D-brane and its expansion. This figure is especially for the decay of a circular D-string ($p=1$) in the background RR 3-form field strength.
  • ...and 12 more figures