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Born-Infeld Strings Tunneling to D-branes

Roberto Emparan

TL;DR

This work investigates whether a Born-Infeld (BI) string, viewed as a collapsed D-brane, can nonperturbatively tunnel to an extended D2-brane configuration in a uniform RR four-form field $h$. Using a cylindrical D2-brane ansatz and a worldvolume flux, the authors derive a reduced BI action and an energy functional, showing that the string can tunnel to either a spheroidal bulge (M2/M2-wrapped interpretation) or a toroidal D2-brane depending on the compactification scale. The decay proceeds through semiclassical instantons, yielding explicit rates for torus nucleation and providing insights into the role of $h$, the string number $n$, and the coupling $g$; the analysis also has a clean M2-brane interpretation and natural extensions to D$p$-branes, with caveats about the BI approximation and neglected backreaction. The results illuminate how BI-string configurations can dynamically transition to genuine brane geometries, offering a nonperturbative bridge between string-like and brane-like descriptions within controlled limits.

Abstract

Recent work on solutions to the Born-Infeld theory used to describe D-branes suggests that fundamental strings can be viewed, in a certain limit, as D-branes whose worldvolumes have collapsed to string-like configurations. Here we address the possibility of undoing this collapse, by inducing the string to tunnel to an extended brane configuration. Using semiclassical methods we argue that, by putting one of these Born-Infeld strings in the background of a uniform 4-form RR field strength, the string can nucleate a spheroidal bulge of D2-brane, or, if the string is wrapped around a small enough circle, it can tunnel to a toroidal D2-brane. This process can also be interpreted in terms of the M2-brane. We also address the extension to other D$p$-branes, and discuss the range of validity of the approximations involved.

Born-Infeld Strings Tunneling to D-branes

TL;DR

This work investigates whether a Born-Infeld (BI) string, viewed as a collapsed D-brane, can nonperturbatively tunnel to an extended D2-brane configuration in a uniform RR four-form field . Using a cylindrical D2-brane ansatz and a worldvolume flux, the authors derive a reduced BI action and an energy functional, showing that the string can tunnel to either a spheroidal bulge (M2/M2-wrapped interpretation) or a toroidal D2-brane depending on the compactification scale. The decay proceeds through semiclassical instantons, yielding explicit rates for torus nucleation and providing insights into the role of , the string number , and the coupling ; the analysis also has a clean M2-brane interpretation and natural extensions to D-branes, with caveats about the BI approximation and neglected backreaction. The results illuminate how BI-string configurations can dynamically transition to genuine brane geometries, offering a nonperturbative bridge between string-like and brane-like descriptions within controlled limits.

Abstract

Recent work on solutions to the Born-Infeld theory used to describe D-branes suggests that fundamental strings can be viewed, in a certain limit, as D-branes whose worldvolumes have collapsed to string-like configurations. Here we address the possibility of undoing this collapse, by inducing the string to tunnel to an extended brane configuration. Using semiclassical methods we argue that, by putting one of these Born-Infeld strings in the background of a uniform 4-form RR field strength, the string can nucleate a spheroidal bulge of D2-brane, or, if the string is wrapped around a small enough circle, it can tunnel to a toroidal D2-brane. This process can also be interpreted in terms of the M2-brane. We also address the extension to other D-branes, and discuss the range of validity of the approximations involved.

Paper Structure

This paper contains 5 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. BI-string from the D2-brane
  3. Static solutions
  4. BI-string decay
  5. Discussion

Figures (2)

  • Figure 1: Static solutions of Born-Infeld theory (in the absence of spacetime background field). A worldvolume electric field runs along the $z$ direction on the D-brane. (a) Spike. (b) Wormhole. (a') Born-Infeld string.
  • Figure 2: Static, unstable configurations in the presence of a uniform background 4-form field strength. The background field tends to pull the D2-brane outwards and balances precisely the elastic tension.