Interaction between two non-threshold bound states

Abstract

A general non-threshold BPS (F, Dp) (or (Dp - 2, Dp)) 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 (mi, ni) with i = 1, 2. With this result, one can show that the non-degenerate (i.e., mi ni ≠ 0) interaction is in general attractive for the case of (Dp - 2, Dp) but this is true and for certain only at large separation for the case of (F, Dp). In either case, this interaction vanishes only if m1/ n1 = m2/ n2 and n1 n2 > 0. We also study the analytic structure of the corresponding amplitude and calculate in particular the rate of pair production of open strings in the case of (F, Dp).