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

We study noncommutative (NC) field theory of a real NC tachyon and NC U(1) gauge field, describing the dynamics of an unstable Dp-brane. For every given set of diagonal component of open string metric G0, NC parameter θ0, and interpolating electric field Ê, 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 D0D̄0 and single stable D0 from the unstable D1, respectively. When the interpolating electric field has critical value as G0 = Ê 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 θ0 and vanishingG0 and Ê, while keeping G0θ0 = Êθ0 = 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 Dp is straightforward for pure electric cases with parallel NC parameter and interpolating two-form field.