Moving Fractional Branes with Background Fields: Interaction and Tachyon Condensation

We calculate the bosonic boundary state corresponding to a moving fractional D$p$-brane in a partially orbifoldized spacetime $\mathbb{R}^{1, d-5} \times\mathbb{C}^{2}/\mathbb{Z}_{2}$ in the presence of the Kalb-Ramond field, the $U(1)$ gauge potential and the tachyon field. Using this boundary state we obtain interaction amplitude of two parallel moving D$p$-branes with the above background fields. Various properties of the interaction will be investigated. Besides, we study effects of the tachyon condensation on a moving fractional D$p$-brane with the above background fields through the boundary state formalism.