[Paper Review] BPS Vortices in Brane-Antibrane Effective Theory

Takao Suyama|ArXiv.org|Dec 30, 2000

Porphyrin and Phthalocyanine Chemistry7 references3 citations

TL;DR

This paper investigates a modified effective field theory of brane-antibrane systems, proposing a BPS vortex solution that saturates the Bogomol'nyi bound and describes a codimension-two D-brane. By introducing a nontrivial kinetic term with exponential dependence on the tachyon field and a specific potential, the model yields smooth, stable first-order vortex equations whose solutions are labeled by topological charge and exhibit quantized energy, consistent with BPS D-brane configurations.

ABSTRACT

We investigate an action which resembles the effective action of brane-antibrane system derived from boundary string field theory. We find that the action has smooth vortex solutions which saturate the Bogomol'nyi bound.

Motivation & Objective

• To investigate whether the effective field theory of a brane-antibrane system admits BPS vortex solutions corresponding to lower-dimensional D-branes.
• To explore the role of nontrivial kinetic terms and a run-away potential in supporting smooth, stable vortex solutions.
• To establish a correspondence between first-order BPS equations and the emergence of codimension-two D-branes in the tachyon condensation framework.

Proposed method

• Formulate a modified effective action with exponential dependence on the tachyon field in the kinetic term and a potential that supports BPS solutions.
• Introduce a complex structure with holomorphic tachyon fields satisfying $ D_{\bar{a}}T = 0 $, ensuring worldsheet supersymmetry.
• Derive first-order BPS equations from the action, including $ D_{\bar{a}}T = 0 $, $ F_{\bar{a}\bar{b}} = 0 $, and a curvature condition involving $ |T|^2 $.
• Analyze the energy density and show it saturates the Bogomol'nyi bound, proving stability.
• Study the asymptotic behavior of solutions in radial coordinates, showing regularity at the origin and linear growth at infinity.
• Demonstrate that the total energy is quantized and proportional to the winding number $ n $, confirming topological stability.

Experimental results

Research questions

• RQ1 Can a modified effective action of the brane-antibrane system support smooth, finite-energy BPS vortex solutions that describe lower-dimensional D-branes?
• RQ2 How do nontrivial kinetic terms—specifically exponential dependence on the tachyon field—affect the existence and stability of BPS vortices?
• RQ3 What is the role of the tachyon's holomorphicity condition $ D_{\bar{a}}T = 0 $ in preserving supersymmetry and enabling BPS solutions?
• RQ4 Why does the standard brane-antibrane action (1.1) fail to support BPS vortices, and how does the modified action resolve this?
• RQ5 How is the topological charge (winding number) related to the quantization of energy and flux in the vortex solution?

Key findings

• The action supports first-order BPS equations that are saturated by smooth, finite-energy vortex solutions with nontrivial profile functions.
• The energy of the solution is quantized and proportional to the winding number $ n $, with $ \mathcal{E} = \frac{2\pi}{g_{YM}^2 a}n $, confirming topological stability.
• Solutions are regular at the origin and exhibit linear asymptotic behavior in radial coordinates, consistent with single-valuedness and finite energy.
• The flux is not quantized in the non-compact case but becomes quantized when the system is compactified, aligning with D-brane charge quantization.
• The tachyon field is holomorphic ($ D_{\bar{a}}T = 0 $), ensuring worldsheet supersymmetry and consistency with string worldsheet analysis.
• The model demonstrates that even with a run-away potential and nontrivial kinetic terms, stable BPS vortices can emerge, providing a viable effective description of D-brane systems.