We derive fully covariant expressions for all two-point scattering amplitudes of two massless closed strings from a Dirichlet p-brane This construction relies on the observation that there is a simple relation between these D-brane amplitudes in type II superstring theory and four-point scattering amplitudes for type I open superstrings. From the two-point amplitudes, we derive the long range background fields for the D-branes, and verify that as expected they correspond to those of extremally charged p-brane solutions of the low energy effective action.

By explicit evaluation of certain disk S-matrix elements in the presence of background B-flux, we find coupling of two open string tachyons to gauge field, graviton, dilaton or Kalb-Ramond antisymmetric tensor on the world-volume of a single non-BPS Dp-brane. We then propose an extension of the abelian Dirac-Born-Infeld action which naturally reproduces these couplings in field theory. This action includes non-linearly the dynamics of the tachyon field much like the other bosonic modes of the non-BPS Dp-brane. On the general grounds of gauge and T-duality transformations and the symmetrized trace prescription, we then extend the abelian action to non-abelian cases.

We study a dark energy scenario in the presence of a tachyon field φ with potential V (φ) and a barotropic perfect fluid. The cosmological dynamics crucially depends on the asymptotic behavior of the quantity λ = −MpV φ /V 3/2 . If λ is a constant, which corresponds to an inverse square potential V (φ) ∝ φ −2 , there exists one stable critical point that gives an acceleration of the universe at late times. When λ → 0 asymptotically, we can have a viable dark energy scenario in which the system approaches an "instantaneous" critical point that dynamically changes with λ. If |λ| approaches infinity asymptotically, the universe does not exhibit an acceleration at late times. In this case, however, we find an interesting possibility that a transient acceleration occurs in a regime where |λ| is smaller than of order unity.

We examine in detail various string scattering amplitudes in order to extract the world-volume interactions of massless fields on a Dirichlet brane. We find that the leading low-energy interactions are consistent with the Born-Infeld and Chern-Simons actions. In particular, our results confirm that the background closed string fields appearing in these actions must be treated as functionals of the non-abelian scalar fields describing transverse fluctuations of the D-brane.Recent years have seen dramatic progress in the understanding of nonperturbative aspects of string theory [1]. With these studies has come the realization that extended objects, other than just strings, play an essential role. An important tool in these investigations has been the Dirichlet brane [2], which within the framework of perturbative string theory provide an exact description of of Ramond-Ramond charged solitons.The world-volume theory of a single D-brane includes a massless U(1) vector A a , a set of massless scalars X i , describing the transverse oscillations of the brane, and their super-partner fermions [3]. The leading order low-energy action for these fields corresponds to a dimensional reduction of a ten dimensional U(1) super-Yang Mills theory. As usual in string theory, there are higher order α ′ = ℓ 2 s corrections, where ℓ s is the string length scale. As long as derivatives of the field strengths (and second derivatives of the scalars) are small compared to ℓ s , then the action takes a Born-Infeld form [4]. This action also has a supersymmetric extension [5]. To take into account the couplings of the open string states with closed strings, the Born-Infeld action can be extended to include background closed string fields, in particular, the metric, dilaton and Kalb-Ramond field. Thus one arrives at the following world-volume action for a Dp-brane:1 Our convention will be that the dilaton field Φ vanishes asymptotically far from the D-branes.