Interaction between two non-threshold bound states

TL;DR

This paper calculates the interaction between two non-threshold bound states characterized by integer pairs, revealing conditions for attraction, repulsion, and zero interaction, and also examines open string pair production rates.

Contribution

It provides explicit formulas for the interaction amplitude between non-threshold bound states with different charge configurations and analyzes their physical implications.

Findings

Interaction is generally attractive for (D_{p-2}, D_p) states.

Interaction vanishes when the ratio of integers matches for both states.

Open string pair production rate is computed for (F, D_p) states.

Abstract

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., $m_i n_i \neq 0$) 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 $m_1/ n_1 = m_2/ n_2$ 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$_p$).