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

## TL;DR

This paper explores zero-modes in a dynamical Dp-brane with background fields using boundary state methods, revealing their significant influence on the system's properties and background interactions.

## Contribution

It introduces a comprehensive analysis of zero-modes for a dynamical Dp-brane across bosonic, fermionic, and superstring frameworks, highlighting their effects on background fields.

## Key findings

- Zero-modes significantly affect background field interactions.
- Analysis across multiple string theory cases provides new insights.
- Zero-modes influence the internal properties of the Dp-brane system.

## Abstract

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.