Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons

Both in string field theory and in p-adic string theory the equations of motion involve infinite number of time derivatives. We argue that the initial value problem is qualitatively different from that obtained in the limit of many time derivatives in that the space of initial conditions becomes strongly constrained. We calculate the energy-momentum tensor and study in detail time dependent solutions representing tachyons rolling on the p-adic string theory potentials. For even potentials we find surprising small oscillations at the tachyon vacuum. These are not conventional physical states but rather anharmonic oscillations with a nontrivial frequency--amplitude relation. When the potentials are not even, small oscillatory solutions around the bottom must grow in amplitude without a bound. Open string field theory resembles this latter case, the tachyon rolls to the bottom and ever growing oscillations ensue. We discuss the significance of these results for the issues of emerging closed strings and tachyon matter.Comment: 46 pages, 14 figures, LaTeX. Replaced version: Minor typos corrected, some figures edited for clarit

Open-Closed Duality at Tree Level

We study decay of unstable D-branes in string theory in the presence of electric field, and show that the classical open string theory results for various properties of the final state agree with the properties of closed string states into which the system is expected to decay. This suggests a duality between tree level open string theory on unstable D-branes and closed strings at high density.Comment: LaTeX file, 10 page

Brane-Antibrane Systems at Finite Temperature and Phase Transition near the Hagedorn Temperature

In order to study the thermodynamic properties of brane-antibrane systems, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. At low temperature, the minimum of the potential shifts towards T=0 as the temperature increases. In the D9-antiD9 case, the sign of the coefficient of |T|^2 term of the potential changes slightly below the Hagedorn temperature. This means that a phase transition occurs near the Hagedorn temperature. On the other hand, the coefficient is kept negative in the Dp-antiDp case with p <= 8, and thus a phase transition does not occur. This leads us to the conclusion that only a D9-antiD9 pair and no other (lower dimensional) brane-antibrane pairs are created near the Hagedorn temperature. We also discuss a phase transition in NS9B-antiNS9B case as a model of the Hagedorn transition of closed strings.Comment: 28 pages, 3 figures, minor errors correcte

Rotating Black Holes which Saturate a Bogomol'nyi Bound

We construct and study the electrically charged, rotating black hole solution in heterotic string theory compactified on a $(10-D)$ dimensional torus. This black hole is characterized by its mass, angular momentum, and a $(36-2D)$ dimensional electric charge vector. One of the novel features of this solution is that for $D >5$, its extremal limit saturates the Bogomol'nyi bound. This is in contrast with the $D=4$ case where the rotating black hole solution develops a naked singularity before the Bogomol'nyi bound is reached. The extremal black holes can be superposed, and by taking a periodic array in $D>5$, one obtains effectively four dimensional solutions without naked singularities.Comment: 13 pages, no figure

Decay of Unstable D-branes with Electric Field

Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.Comment: 35 pages, LaTe

Finite Temperature Systems of Brane-Antibrane on a Torus

In order to study the thermodynamic properties of brane-antibrane systems in the toroidal background, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. We first consider the case that all the radii of the target space torus are about the string scale. If the Dp-antiDp pair is extended in all the non-compact directions, the sign of the coefficient of |T|^2 term of the potential changes slightly below the Hagedorn temperature. This means that a phase transition occurs near the Hagedorn temperature. On the other hand, if the Dp-antiDp pair is not extended in all the non-compact directions, the coefficient is kept negative, and thus a phase transition does not occur. Secondly, we consider the case that some of the radii of the target space torus are much larger than the string scale and investigate the behavior of the potential for each value of the radii and the total energy. If the Dp-antiDp pair is extended in all the non-compact directions, a phase transition occurs for large enough total energy.Comment: 23 pages, 3 figures, minor errors corrected, version to appear in JHE

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

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.Comment: Latex, 14 pages, 1 figure, the version appears in JHE

The Tachyon Inflationary Models with Exact Mode Functions

We show two analytical solutions of the tachyon inflation for which the spectrum of curvature (density) perturbations can be calculated exactly to linear order, ignoring both gravity and the self-interactions of the tachyon field . The main feature of these solutions is that the spectral indices are independent with scale.Comment: 5 pages, no figure, to appear in Phys. Rev.

Hybrid Inflation and Brane-Antibrane System

We study a string theory inspired model for hybrid inflation in the context of a brane-antibrane system partially compactified on a compact submanifold of (a caricature of) a Calabi-Yau manifold. The interbrane distance acts as the inflaton, whereas the end of the inflationary epoch is brought about by the rapid rolling of the tachyon. The number of e-foldings is sufficiently large and is controlled by the initial conditions. The slow roll parameters, however, are essentially determined by the geometry and have little parametric dependence. Primordial density fluctuations can be made consistent with current data at the cost of reducing the string scale.Comment: 22 pages, 7 Figs (added a Report-no and two references

Cosmological Scaling Solutions of Multiple Tachyon Fields with Inverse Square Potentials

We investigate cosmological dynamics of multiple tachyon fields with inverse square potentials. A phase-space analysis of the spatially flat FRW models shows that there exists power-law cosmological scaling solutions. We study the stability of the solutions and find that the potential-kinetic-scaling solution is a global attractor. However, in the presence of a barotropic fluid the solution is an attractor only in one region of the parameter space and the tracking solution is an attractor in the other region. We briefly discuss the physical consequences of these results.Comment: 10 pages, 1 figure, LaTeX2