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We investigate the BPS configuration of the multi D-vortices produced from the D2${bar {rm D}}$2 system. Based on the DBI-type action with a Gaussian-type runaway potential for a complex tachyon field, the BPS limit is achieved when the tachyon profile is thin. The solution states randomly-distributed $n$ static D-vortices with zero interaction. With the obtained BPS configuration, we derive the relativistic Lagrangian which describes the dynamics of free massive D-vortices. We also discuss the 90${}^{circ}$ and 180${}^{circ}$ scattering of two identical D-vortices, and present its implications on the reconnection in the dynamics of cosmic superstrings.
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Moduli space dynamics of multi-D-vortices from D2${bar {rm D}}$ (equivalently, parallel straight D-strings from D3${bar {rm D}}$3) is systematically studied. For the BPS D-vortices, we show through exact calculations that the classical motion of randomly-distributed $n$ D-vortices is governed by a relativistic Lagrangian of free massive point-particles. When the head-on collision of two identical BPS D-vortices of zero radius is considered, it predicts either 90${}^{circ}$ scattering or 0${}^{circ}$ scattering equivalent to 180${}^{circ}$ scattering. Since the former leads to a reconnection of two identical D-strings and the latter does to a case of their passing through each other, two possibilities are consistent with the prediction of string theory. It is also shown that the force between two non-BPS vortices is repulsive. Although the obtained moduli space dynamics of multi-BPS-D-vortices is exact in classical regime, the quantum effect of an F-string pair production should be included in determining the probabilities of the reconnection and the passing through for fast-moving cosmic superstrings.
We derive the BPS mass formulae of the Dirichlet branes from the Born-Infeld type action. BPS saturation is realized when the brane has the minimal volume while keeping the appropriate winding numbers. We apply the idea to two cases, type IIA superstring compactified on $T^4$ and $K3$. The result is consistent with the string duality, and the expected spectrum for the BPS states is reproduced.
We review the boundary state description of the non-BPS D-branes in the type I string theory and show that the only stable configurations are the D-particle and the D-instanton. We also compute the gauge and gravitational interactions of the non-BPS D-particles and compare them with the interactions of the dual non-BPS particles of the heterotic string finding complete agreement. In this way we provide further dynamical evidence of the heterotic/type I duality.
We assume that the early universe is homogeneous, anisotropic, and is dominated by the mutually BPS 2255 intersecting branes of M theory. The spatial directions are all taken to be toroidal. Using analytical and numerical methods, we study the evolution of such an universe. We find that, asymptotically, three spatial directions expand to infinity and the remaining spatial directions reach stabilised values. Any stabilised values can be obtained by a fine tuning of initial brane densities. We give a physical description of the stabilisation mechanism. Also, from the perspective of four dimensional spacetime, the effective four dimensional Newtons constant G_4 is now time varying. Its time dependence will follow from explicit solutions. We find in the present case that, asymptotically, G_4 exhibits characteristic log periodic oscillations.
We study the gauge and gravitational interactions of the stable non-BPS D-particles of the type I string theory. The gravitational interactions are obtained using the boundary state formalism while the SO(32) gauge interactions are determined by evaluating disk diagrams with suitable insertions of boundary changing (or twist) operators. In particular the gauge coupling of a D-particle is obtained from a disk with two boundary components produced by the insertion of two twist operators. We also compare our results with the amplitudes among the non-BPS states of the heterotic string which are dual to the D-particles. After taking into account the known duality and renormalization effects, we find perfect agreement, thus confirming at a non-BPS level the expectations based on the heterotic/type I duality.
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