Interaction of Dynamical Fractional Branes with Background Fields: Superstring Calculations

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.