Dynamics and stability of light-like tachyon condensation

Abstract

Recently, Hellerman and Schnabl considered the dynamics of unstable D-branes in the background of a linear dilaton. Remarkably, they were able to construct light-like tachyon solutions which interpolate smoothly between the perturbative and nonperturbative vacua, without undergoing the wild oscillations that plague time-like solutions. In their analysis, however, the full structure of the initial value problem for the nonlocal dynamical equations was not considered. In this paper, therefore, we reexamine the nonlinear dynamics of lightlike tachyon condensation using a combination of numerical and analytical techniques. We find that for the p-adic string the monotonic behaviour obtained previously relied on a special choice of initial conditions near the unstable maximum. For generic initial conditions the wild oscillations come back to haunt us. Interestingly, we find an "island of stability" in initial condition space that leads to sensible evolution at late times. For the string field theory case, on the other hand, we find that the evolution is completely stable for generic choices of initial data. This provides an explicit example of a string theoretic system that admits infinitely many initial data but is nevertheless nonperturbatively stable. Qualitatively similar dynamics are obtained in nonlocal cosmologies where the Hubble damping plays a role very analogous to the dilaton gradient.

Quintom cosmology: Theoretical implications and observations

“…In such a context a rolling tachyon field in the world volume theory of the open string, stretched between a D-brane and an anti-D-brane or a non-BPS D-brane, plays the role of the scalar field in the quintom model [101,211,212,213,214,215,216,217]. The effective action used in the study of tachyon cosmology consists of the standard EinsteinHilbert action plus an effective action for the tachyon field on unstable D-brane or (D-brane)-(anti-D-brane) system.…”

Fisher equation for a decaying brane

“…One could proceed in another way to avoid this problem. We notice that the interaction term involves: 6) and folding by the Gaussian kernel softens the oscillations. Since, in the limit, a → 0, the kernel becomes the Dirac δ-function,…”

“…Since then, these conjectures have been checked in the open string field theory in the level truncation scheme, in various toy models, in the boundary string field theory, and finally, an exact solution describing the state at the (local) minimum of the tachyon potential has been constructed in open string field theory. Much less studied, however, is the time-dependent dynamical process of tachyon condensation [2][3][4][5][6][7][8][9].…”

Travelling front of a decaying brane in string field theory

“…While time-dependent processes in string theory are difficult to analyze in general, the process of tachyon rolling down the potential is one in which certain aspects of dynamics have been found to be tractable [2][3][4][5][6][7]. In particular, the pioneering studies in ref.…”