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Supergravity Description of Non-BPS Branes

Philippe Brax, Gautam Mandal, Yaron Oz

TL;DR

This work constructs localized Type II supergravity backgrounds for bound states of N Dp-branes with N̄ anti-Dp-branes and interprets a third integration constant as the closed-string manifestation of the open-string tachyon vev. By analyzing the ADM mass and RR charge, the authors relate c1 to the tachyon potential V(T) and show that c1=0 corresponds to V(T)=0, i.e., T at the maximum; small deformations in c1 reproduce the near-origin behavior of V(T). They also demonstrate that the four-parameter extension yields a rich phase diagram connecting brane–antibrane configurations, BPS branes, black branes, and Schwarzschild black holes, with an interpolating sector (the BC arm) bridging brane–antibrane solutions and Schwarzschild geometry. A decoupling limit is not achieved for the neutral case, indicating persistent open–closed string interactions and limiting a purely field-theoretic (open string) description of tachyon condensation. The results offer a framework for studying non-supersymmetric black holes and brane dynamics beyond BPS configurations, motivating further work on explicit mappings between open-string tachyon data and closed-string supergravity parameters.

Abstract

We construct supergravity solutions that correspond to N Dp-branes coinciding with \bar{N} \bar{Dp}-branes. We study the physical properties of the solutions and analyse the supergravity description of tachyon condensation. We construct an interpolation between the brane-antibrane solution and the Schwarzschild solution and discuss its possible application to the study of non-supersymmetric black holes.

Supergravity Description of Non-BPS Branes

TL;DR

This work constructs localized Type II supergravity backgrounds for bound states of N Dp-branes with N̄ anti-Dp-branes and interprets a third integration constant as the closed-string manifestation of the open-string tachyon vev. By analyzing the ADM mass and RR charge, the authors relate c1 to the tachyon potential V(T) and show that c1=0 corresponds to V(T)=0, i.e., T at the maximum; small deformations in c1 reproduce the near-origin behavior of V(T). They also demonstrate that the four-parameter extension yields a rich phase diagram connecting brane–antibrane configurations, BPS branes, black branes, and Schwarzschild black holes, with an interpolating sector (the BC arm) bridging brane–antibrane solutions and Schwarzschild geometry. A decoupling limit is not achieved for the neutral case, indicating persistent open–closed string interactions and limiting a purely field-theoretic (open string) description of tachyon condensation. The results offer a framework for studying non-supersymmetric black holes and brane dynamics beyond BPS configurations, motivating further work on explicit mappings between open-string tachyon data and closed-string supergravity parameters.

Abstract

We construct supergravity solutions that correspond to N Dp-branes coinciding with \bar{N} \bar{Dp}-branes. We study the physical properties of the solutions and analyse the supergravity description of tachyon condensation. We construct an interpolation between the brane-antibrane solution and the Schwarzschild solution and discuss its possible application to the study of non-supersymmetric black holes.

Paper Structure

This paper contains 11 sections, 74 equations, 5 figures.

Table of Contents

  1. Introduction
  2. The Supergravity Description
  3. The Supergravity Solution
  4. Physical Properties
  5. Tachyon Condensation
  6. ${\langle {\rm T} \rangle}$ in Supergravity
  7. Dp-brane probes and Binding energy
  8. Open-closed String Duality
  9. The Four-Parameter Solution
  10. Discussion
  11. Details of the 4-parameter solution

Figures (5)

  • Figure 1: The $M,c_1$ plane for a given fixed $Q \neq 0$. The BPS solution corresponds to the scaled neighbourhood represented by the shaded circle. Path II represents decay to a BPS D-brane of charge $Q$.
  • Figure 2: The two-parameter space of solutions for $Q=0$, as parameterised by $M,c_1$. Path II represents decay of the brane-antibrane configuration to flat space.
  • Figure 3: ADM Mass (for a fixed $r_0>0$) as a function of (a) $c_1$ and (b) $|T|$
  • Figure 4: The scattering potential $V(r)$ for gravitons on D$p$-$\overline{{\rm D} p}$-branes.
  • Figure 5: The most general spherically symmetric solution of Type II theories