Some Non-Perturbative Aspects Of String/M Theory

We study some non-perturbetive aspects of the string/M theory.Firstly,we study the interactions between coincident brane and anti-brane from both open string description as well as supergravity description.Secondly,we study the low energy dynamical behavior of brane/anti-brane system.Thirdly,we calculate explicitly the interaction amplitude between two non-threshold BPS bound states.For brane-antibrane forces,in one aspect,we generalize the force calculation of DO-(?)O of Banks and Susskind to Dp-(?)p for 1≤p≤8.The forces are divergent for all cases when the brane-antibrane separation approaches to the string scale,signalling the occurrence of open string tachyon condensation in this regime.In the other aspect we deal with the puzzling static nature of the supergravity brane-antibrane configurations. We will show that the force on a brane probe due to a brane-antibrane background vanishes when the probe is placed at the location of the coincident brane-antibranes, thereby providing a direct evidence for the existence of general static brane-antibrane configuration in the supergravity approximation.We also study the dynamical behavior of a pair of Dp-brane and anti Dp-brane (0≤p≤6) moving parallel to each other in the region where the brane and anti-brane annihilation will not occur and the low energy description is valid.Given this,we perform a general analysis,in the center of mass frame,of the behavior of the effective potential with respect to the relative brane separation and find that the classical orbits of this system are in general unbound except for p = 6 case for which classical bound orbits exist.The non-linearity of the low energy DBI action for D-brane is important for the underlying dynamics.We solve also the explicit orbits for p = 6 case.A general non-threshold BPS(F,D_p)(or(D_p-2,D_p)) bound state can be described by a boundary state with a quantized world-volume electric(or magnetic) flux and is characterized by a pair of integers(m,n).With this,we calculate explicitly the interaction amplitude between two such non-threshold bound states with a separation Y when each of the states is characterized by a pair of integers(m_i,n_i) with i = 1,2. With this result,one can show that the non-degenerate(i.e.,m_in_i≠0) interaction is in general attractive for the case of(D_p-2,D_p) but this is true and for certain only at large separation for the case of(F,D_p).In either case,this interaction vanishes only if m₁/n₁ = m₂/n₂ and n₁n₂＞0.We also study the analytic structure of the corresponding amplitude and the pair production of open strings in the case of(F,D_p).