# Interaction of Dynamical Fractional Branes with Background Fields: Superstring Calculations

## TL;DR

This paper calculates the boundary state for fractional Dp-branes with background fields and motion in a superstring framework, analyzing their interactions and behavior at large distances.

## Contribution

It introduces a method to compute boundary states for fractional D-branes with background fields and motion in superstring theory, enabling analysis of their interactions.

## Key findings

- Derived the boundary state for fractional D-branes with background fields.
- Calculated the interaction amplitude between two moving fractional D-branes.
- Analyzed the large-distance behavior of the interaction amplitude.

## Abstract

We compute the boundary state corresponding to a fractional D$p$-brane with transverse motion and internal background fields: Kalb-Ramond and a $U(1)$ gauge field. The spacetime has the orbifold structure $\mathbb{R}^{1,5} \times\mathbb{C}^{2}/\mathbb{Z}_{2}$. The calculations are in the superstring theory. Using this boundary state we shall obtain the interaction amplitude between two parallel moving fractional D$p$-branes. We shall extract behavior of the interaction amplitude for large distances of the branes.