# On D-brane interaction & its related properties

## TL;DR

This paper calculates the interaction amplitude between parallel Dp and Dp' branes with fluxes, revealing how flux types influence stability, interaction nature, and pair production, and provides a general formula for these amplitudes.

## Contribution

It derives a comprehensive general formula for D-brane interaction amplitudes with fluxes, covering various p-p' configurations and flux types, including pair production rates.

## Key findings

- Interaction nature depends on flux type: attractive with tachyonic instability, repulsive without.
- Pure electric fluxes can enhance open string pair production, especially for p-p' = 2.
- The general amplitude formula applies to multiple brane configurations with arbitrary fluxes.

## Abstract

We compute the closed-string cylinder amplitude between one Dp brane and the other Dp$\prime$ brane, placed parallel at a separation, with each carrying a general constant worldvolume flux and with $p - p' = 0, 2, 4, 6$ and $p \le 6$. For the $p = p'$, we show that the main part of the amplitude for $p = p' < 5$ is a special case of that for $p = p' = 5$ or $6$ case. For all other $p - p' = 2, 4, 6$ cases, we show that the amplitude is just a special case of the corresponding one for $p = p'$ case. Combining both, we obtain the general formula for the amplitude, which is valid for each of the cases considered and for arbitrary constant worldvolume fluxes. The corresponding general open string one-loop annulus amplitude is also obtained by a Jacobi transformation of the general cylinder one. We give also the general open string pair production rate. We study the properties of the amplitude such as the nature of the interaction, the open string tachyonic instability, and the possible open string pair production and its potential enhancement. In particular, in the presence of pure magnetic fluxes or magnetic-like fluxes, we find that the nature of interaction is correlated with the existence of potential open string tachyonic instability. When the interaction is attractive, there always exists an open string tachyonic instability when the brane separation reaches the minimum determined by the so-called tachyonic shift. When the interaction is repulsive, there is no such instability for any brane separation. We also find that the enhancement of open string pair production, in the presence of pure electric fluxes, can occur only for the $p - p' = 2$ case.