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

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.