Interaction between two nonthreshold bound states

Abstract

A general nonthreshold Bogomol'nyi-Prasad-Sommerfield $(F,{D}_{p})$ [or $({D}_{p\ensuremath{-}2},{D}_{p})$] 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 nonthreshold 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 nondegenerate (i.e., ${m}_{i}{n}_{i}\ensuremath{\ne}0$) interaction is, in general, attractive for the case of $({D}_{p\ensuremath{-}2},{D}_{p})$, 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 ${m}_{1}/{n}_{1}={m}_{2}/{n}_{2}$ and ${n}_{1}{n}_{2}>0$. 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 $(F,{D}_{p})$.