Fractional-Wrapped Branes with Rotation, Linear Motion and Background Fields

TL;DR

This paper constructs boundary states for fractional-wrapped Dp-branes with rotation, motion, and background fields, and analyzes their interaction amplitudes in an orbifolded spacetime, revealing long-range interaction properties.

Contribution

It introduces a detailed boundary state formulation for fractional-wrapped Dp-branes with rotation, motion, and background fields in orbifolded spacetime, and computes their interaction amplitudes.

Findings

Interaction amplitude analyzed for long-range behavior

Boundary states constructed for twisted and untwisted sectors

Properties of brane interactions in complex background fields

Abstract

We obtain two boundary states corresponding to the two folds of a fractional-wrapped D$p$-brane, i.e. the twisted version under the orbifold $\mathbb{C}^{2}/\mathbb{Z}_{2}$ and the untwisted version. The brane has rotation and linear motion, in the presence of the following background fields: the Kalb-Ramond tensor, a $U(1)$ internal gauge potential and a tachyon field. The rotation and linear motion are inside the volume of the brane. The brane lives in the $d$-dimensional spacetime, with the orbifold-toroidal structure $T^n \times \mathbb{R}^{1, d-n-5} \times\mathbb{C}^{2}/\mathbb{Z}_{2}$ in the twisted sector. Using these boundary states we calculate the interaction amplitude of two parallel fractional D$p$-branes with the foregoing setup. Various properties of this amplitude such as the long-range behavior will be analyzed.