Left-Right Entanglement Entropy for a Dp-brane with Dynamics and Background Fields

We investigate the left-right entanglement entropy of a boundary state, corresponding to a dynamical D$p$-brane with the internal and background fields. We assume that the brane has a tangential linear motion and a rotation, and is dressed with an internal $U(1)$ gauge potential and the Kalb-Ramond tensor field $B_{\mu \nu }$. We derive the entanglement entropy via the R'{e}nyi entropy by applying the replica trick. Our calculations will be in the context of the bosonic string theory.