Investigation of Zero-Modes for a Dynamical D$p$-Brane

In this article, we investigate zero-modes for a dynamical (rotating-moving) D$p$-brane, coupled to the electromagnetic and tachyonic background fields. This work is done by the boundary state methods, in three cases of bosonic and fermionic boundary states and superstring partition function. By analyzing the obtained zero-modes in either of the cases, interesting results will be obtained. Our findings demonstrate the importance of the zero-mode and its effects on the background fields and the defined internal properties of the described system.