LREE of a Dressed D$p$-brane with Transverse Motion in the Partially Compact Spacetime

In the context of the type IIA/IIB superstring theories, we derive the left-right entanglement entropy (LREE) of a BPS D$p$-brane with transverse motion in the presence of a $U(1)$ gauge potential and the Kalb-Ramond field in the partially compact spacetime $\mathbf{T}^n \otimes \mathbb R^{1,9-n}$. At first we employ the replica trick to compute the R\'{e}nyi entropy and then we obtain the entanglement entropy. We examine the results for the special case, i.e. for the D6-brane. Besides, we investigate the thermodynamical entropy, associated with the LREE. This demonstrates that the LREE is precisely equivalent to its thermodynamic counterpart.