D-brane anti-D-brane effective action and brane interaction in open string channel

TL;DR

This paper develops an effective action for D-brane anti-D-brane systems using non-abelian tachyonic DBI theory, analyzing the potential and interaction dynamics as branes approach or separate.

Contribution

It constructs a new effective action for D-brane anti-D-brane systems by extending tachyonic DBI theory and analyzing the potential landscape for brane interactions.

Findings

Potential has two minima when branes are far apart.

Tachyon tunneling can lead to bubble formation during brane collision.

Classical tachyon rolling induces an attractive 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.