[Paper Review] D-brane anti-D-brane effective action and brane interaction in open string channel

Garousi, Mohammad R.|arXiv (Cornell University)|Nov 24, 2004

Black Holes and Theoretical Physics44 citations

TL;DR

This paper constructs a non-abelian effective action for Dp-$\bar{D}$p brane systems using the tachyonic DBI action with restricted Chan-Paton factors, showing that brane separation relative to the string scale determines the tachyon potential's structure: two minima for large separations (tunneling via instantons), one minimum and maximum for small separations (classical tachyon rolling). The resulting classical force from rolling tachyons is proposed as the effective interaction force between branes.

ABSTRACT

We construct the effective action of a $D_p$-brane-anti-$D_p$-brane system by making use of the non-abelian extension of tachyonic DBI action. We succeed the construction by restricting the Chan-Paton factors of two non-BPS $D_p$-branes in the action to the Chan-Paton factors of a $D_p\bar{D}_p$ system. For the special case that both branes are coincident, the action reduces to the one proposed by A. Sen. \\The effective $D_p\bar{D}_p$ potential indicates that when branes separation is larger than the string length scale, there are two minima in the tachyon direction. As branes move toward each other under the gravitational force, the tachyon tunneling from false to true vacuum may make a bubble formation followed by a classical evolution of the bubble. On the other hand, when branes separation is smaller than the string length scale, the potential shows one maximum and one minimum. In this case, a homogeneous tachyon rolling in real time makes an attractive potential for the branes distance. This classical force is speculated to be the effective force between the two branes.

Motivation & Objective

• To derive a unified effective action for Dp-$\bar{D}$p brane systems valid across different brane separations.
• To describe both the decay dynamics (via tachyon condensation) and the classical interaction force between branes in a single framework.
• To clarify the transition between open and closed string channel descriptions based on brane separation relative to the string scale.
• To identify the effective force between branes arising from homogeneous tachyon rolling in the open string channel when separation is small.

Proposed method

• Derive the effective action by restricting Chan-Paton factors of two non-BPS Dp-branes in the non-abelian tachyonic DBI action to those of a Dp-$\bar{D}$p system.
• Use the non-abelian tachyonic DBI action as a starting point, which is known to reproduce string S-matrix elements for non-BPS D-branes.
• Simplify the action by assuming trivial background, homogeneous tachyon, and separation only in one transverse direction (k-th direction).
• Extract the effective potential V(φ, ℓ) from the simplified action, where φ is the tachyon field and ℓ is the brane separation.
• Analyze the potential's structure (minima, maxima) to determine whether tachyon tunneling (non-perturbative) or rolling (classical) dominates based on ℓ.
• Propose that the classical force arising from homogeneous tachyon rolling in the ℓ-direction is the effective interaction force for small separations.

Experimental results

Research questions

• RQ1 How does the tachyon potential for a Dp-$\bar{D}$p system depend on brane separation relative to the string scale?
• RQ2 What determines whether tachyon decay proceeds via tunneling (instanton) or classical rolling?
• RQ3 Can a classical force emerge from tachyon dynamics that acts as the effective interaction between branes?
• RQ4 How does the effective action unify the description of brane decay and interaction in different regimes?
• RQ5 What is the role of the tachyon field in generating an effective attractive force between branes when separation is small?

Key findings

• For brane separation ℓ > √(2π²α′), the tachyon potential V(φ, ℓ) has two minima: one at φ = 0 and another at φ → ∞, indicating a false vacuum and a true vacuum.
• For ℓ < √(2π²α′), the potential has one maximum and one minimum in the tachyon direction, allowing for a homogeneous classical tachyon rolling solution.
• The classical force arising from homogeneous tachyon rolling is proposed as the effective interaction force between branes in the open string channel for small separations.
• When ℓ > √(2π²α′), the system cannot classically roll through the barrier, so decay proceeds via non-perturbative tachyon tunneling (instanton) with a bounce solution forming a bubble.
• The effective potential is symmetric under φ → −φ and ℓ → −ℓ, indicating a symmetric double-well structure for large separations.
• The cosmological implications suggest that initial conditions near ℓ ≈ √(2π²α′) could lead to enhanced e-foldings in tachyon-driven inflation models.