Non Abelian Geometrical Tachyon

TL;DR

This paper explores the non-abelian geometric tachyon dynamics of coincident D5 branes in NS5 brane backgrounds, extending the duality proposal and analyzing solutions that describe bouncing brane configurations.

Contribution

It extends Kutasov's duality proposal to the non-abelian case, introducing matrix-valued fields and analyzing the resulting equations of motion and solutions.

Findings

Duality holds with matrix-valued radial fields in non-abelian case.

Analytic and numerical solutions show periodic 'bouncing' motion.

Solutions describe a finite-sized throat with minimal separation.

Abstract

We investigate the dynamics of a pair of coincident D5 branes in the background of $k$ NS5 branes. It has been proposed by Kutasov that the system with a single probing D-brane moving radially in this background is dual to the tachyonic DBI action for a non-BPS Dp brane. We extend this proposal to the non-abelian case and find that the duality still holds provided one promotes the radial direction to a matrix valued field associated with a non-abelian geometric tachyon and a particular parametrization for the transverse scalar fields is chosen. The equations of motion of a pair of coincident D5 branes moving in the NS5 background are determined. Analytic and numerical solutions for the pair are found in certain simplified cases in which the U(2) symmetry is broken to $U(1) \times U(1)$ corresponding to a small transverse separation of the pair. For certain range of parameters these solutions describe periodic motion of the centre of mass of the pair 'bouncing off' a finite sized throat whose minimum size is limited by the D5 branes separation.