Noncommutative Tachyon Kinks as D$(p-1)$-branes from Unstable D$p$-brane

TL;DR

This paper constructs exact noncommutative tachyon kink solutions on unstable D-branes, identifying them as lower-dimensional D-branes, and explores their properties, including tension, charge, and BPS conditions, in various limits.

Contribution

It provides a comprehensive classification of static noncommutative tachyon kink solutions and their interpretation as D-branes, including BPS states, in the context of unstable D$p$-branes.

Findings

Exact static NC kink solutions classified by kink-antikink and topological types.

Identified configurations as D0, D0-anti-D0 pairs, and BPS D0 in string fluid.

Finiteness of tension in certain limits corresponds to tensionless kinks in effective field theory.

Abstract

We study noncommutative (NC) field theory of a real NC tachyon and NC U(1) gauge field, describing the dynamics of an unstable D$p$-brane. For every given set of diagonal component of open string metric $G_{0}$, NC parameter $\theta_{0}$, and interpolating electric field ${\hat E}$, we find all possible static NC kinks as exact solutions, in spite of complicated NC terms, which are classified by an array of NC kink-antikink and topological NC kinks. By computing their tensions and charges, those configurations are identified as an array of D0${\bar {\rm D}}$0 and single stable D0 from the unstable D1, respectively. When the interpolating electric field has critical value as $G_{0}^{2}={\hat E}^{2}$, the obtained topological kink becomes a BPS object with nonzero thickness and is identified as BPS D0 in the fluid of fundamental strings. Particularly in the scaling limit of infinite $\theta_{0}$ and vanishing $G_{0}$ and ${\hat E}$, while keeping $G_{0}\theta_{0}={\hat E}\theta_{0}=1$, finiteness of the tension of NC kink corresponds to tensionless kink in ordinary effective field theory. An extension to stable D$(p-1)$ from unstable D$p$ is straightforward for pure electric cases with parallel NC parameter and interpolating two-form field.