Origin of the geometric tachyon

Abstract

The motion of a Dp-brane in the background of a stack of coincident NS5-branes is analyzed as the motion of a relativistic point particle in the transverse space of the five-branes. In this system, the particle experiences a proper acceleration orthogonal to its proper velocity due to the background dilaton field which changes the dynamics from that of a simple geodesic motion. In particular, we show that in the vicinity of the five-branes, it is this acceleration which is responsible for modifying the motion of the radial mode to that of an inverted simple harmonic oscillator leading to the tachyonic instability. 11.25.Uv, 04.65.+e In string theory, it is well-known that soliton solutions like the NS5-brane and Dp-brane are contained in the string spectrum. While the former is supersymmetric and stable, the latter can be either supersymmetric and stable (BPS Dp-brane) or non-supersymmetric and unstable (non-BPS Dp-brane). A pair of D-D branes is non-supersymmetric even if each is supersymmetric individually. Such non-supersymmetric systems are unstable because the lowest lying state of the open string, either (both ends) ending on a single non-BPS D-brane or stretched between the brane and the antibrane, is a tachyon. The condensation of the tachyon can lead to a stable brane configuration or the total annihilation of the brane. A nice review of this phenomenon can be found in [1]. The dynamics of tachyon condensation has led to many interesting time dependent phenomena including the decay of a non-BPS brane into a strange "tachyon matter" state whose equation of state is that of a pressureless fluid [2]. An effective action of the Dirac-BornInfeld (DBI) type for the tachyon [3,4,5,6] has been very useful in understanding such processes.A completely different dynamics, namely, that of a BPS Dp-brane propagating in the background of a stack of coincident NS5-branes, has been studied recently using the effective DBI action [7]. It has been observed there that when the Dp-brane comes close to the NS5-branes, the dynamics of the Dp-brane can be mapped to that of the open string tachyon condensation, where the radial mode on the Dp-brane plays the role of the tachyon. Moreover, its equation of state approaches that of a pressureless fluid with the pressure falling off exponentially at late times. These properties along with the fact that a parallel Dp-NS5 brane system is a nonsupersymmetric system, has led to the nomenclature "geometric tachyon" for the radial mode on the Dp-brane. The tachyonic instability has been made more precise [8] by compactifying one of the transverse directions of * e-mails: das@pas.rochester.edu, panda@mri.ernet.in, shibaji.roy@saha.ac.in the NS5-branes on a circle and placing the Dp-brane, as a point on this circle diametrically opposite to the fivebranes. In such a case it has been observed that the potential energy density of the Dp-brane at this point has a saddle point. As a result, this point corresponds to an unstable equilibrium and the Dp-brane develops a tachyonic mode associ...

Proper acceleration, the geometric tachyon and the dynamics of a fundamental string near D p branes

“…. , 9 and G AB and B AB are the metric and the B-field in ten dimensions, given in (28). We are interested in the case when the fields representing the position of the Dp-brane X m , m = 6, .…”

Fundamental String (Membrane) Orbiting D5(m5)-Branes

“…In an attempt to understand the origin of this geometric tachyon in [17] the time dependent dynamics of probe D-brane in the background of NS5-brane was explained in terms of proper acceleration. It was proposed that the tachyonic instability is due to the geodesic deviation caused by proper acceleration (which is formed due to the background dilaton field).…”

Geometric Tachyon and Warm Inflation

“…In this system, the particle experiences a proper acceleration orthogonal to its proper velocity due to the background dilaton field which changes the dynamics from that of a simple geodesic motion. In particular, it is shown that in the vicinity of the five-branes, it is this acceleration which is responsible for modifying the motion of the radial mode to that of an inverted simple harmonic oscillator leading to the tachyonic instability [20,21].…”