Interaction between two nonthreshold bound 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 = 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 ).

A Classification of Long-Range Interactions between Two Stacks of p & p′ -Branes

“…In some special cases such as those involved p-branes and their Hodge-dual objects, the explicit results can also be given in diverse dimensions. Combined with the known parallel cases [1,2,8], we give a classification of long-range interactions for simple branes. This serves as a dictionary and is useful when we consider more complicated brane systems such as the brane bound states for which the nature of interaction (attractive or repulsive) can often be simply read from this dictionary without the need of detail computations.…”

“…For the two systems, there are ten cases for either q = 2 or q = 3 but there is only one case for either of them for which the interaction cannot be simply read from the dictionary. We then calculate the corresponding interaction using the couplings derived in [1,8] and discuss how the nature of interaction depends on the fluxes on the branes. We also provide two tables given in the appendix showing the nature of the long-range interaction between two stacks of D-branes placed non-parallel with each carrying a constant k = 1 magnetic flux.…”

“…As we know that D-branes carrying a single abelian electric or magnetic world volume flux are the non-threshold BPS (F, Dp) bound state [12,13,14,15,16,17] or the non-threshold BPS (D(p − 2), Dp) bound state [18,19,20], respectively. The long-range interaction between two parallel D-branes with each carrying an abelian world-volume flux has been discussed in [8]. There are also other D-brane bound states (D(p − 2k), Dp) with k = 2, 3, 4, respectively.…”

“…to denote the cases for which the total interaction cannot be determined by the prescription given above and we must do the computations to determine the nature of the underlying long-range interaction. This can be done without much difficulty following the couplings given in [1,8]. There actually exists only one case for either q = 2 or q = 3 as shown in the corresponding table.…”

“…There actually exists only one case for either q = 2 or q = 3 as shown in the corresponding table. We just quote the couplings needed for this computations from [1,8] as…”