# Interaction of the branes in the Presence of the Background Fields: the Dynamical Non-intersecting Perpendicular Wrapped-Fractional Configuration

## TL;DR

This paper calculates the interaction between non-intersecting, perpendicular, dynamical fractional D-branes with background fields in a specific toroidal-orbifold spacetime, analyzing the long-range behavior of their interaction amplitude.

## Contribution

It introduces a detailed boundary state formalism for dynamical fractional D-branes with background fields in a complex orbifold setting, extending previous models.

## Key findings

- Derived the bosonic boundary state for fractional D-branes with background fields.
- Analyzed the long-range interaction amplitude between such branes.
- Provided insights into the effects of background fields on brane interactions.

## Abstract

We shall obtain the interaction of the D$p_1$- and D$p_2$-branes in the toroidal-orbifold spacetime $\mathit{T}^{n}\times\mathbb{R}^{1, d-n-5} \times\mathbb{C}^{2}/\mathbb{Z}_{2}$. The configuration of the branes is: non-intersecting, perpendicular, moving-rotating, wrapped-fractional with background fields. For this, we calculate the bosonic boundary state corresponding to a dynamical fractional-wrapped D$p$-brane in presence of the Kalb-Ramond field, a $U(1)$ gauge potential and an open string tachyon field. The long-range behavior of the interaction amplitude will be extracted.