Noncommutative tachyon kinks as D(p-1)-branes from unstable Dp-brane -: art. no. 023

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 G(0), NC parameter theta(0), and interpolating electric field (E) over cap, 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 (D) over bar0 and single stable D0 from the unstable D1, respectively. When the interpolating electric field has critical value as G(0)(2) = (E) over cap (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 (E) over cap, while keeping G(0)theta(0) = (E) over cap theta(0) = 1, finiteness of 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.