Exact BPS kink in BCFT, DBI EFT, NCFT, and BSFT

We discuss single topological BPS kinks with non-zero thickness, which are exact solutions in various contexts including Dirac-Born-Infeld type effective field theory, noncommutative field theory, boundary conformal field theory, and boundary string field theory. The tachyon field is monotonically increasing (or decreasing) and connects the isolated vacua at positive and negative infinity irrespective of the theories of our interest. It is expressed by a simple linear function, τ(X) ∝ X, in the case of boundary conformal field theory. The obtained tachyon kink in the presence of critical electromagnetic field is interpreted as a single thick BPS D(p-1)-brane (or D(p - 1)F1-composite) inside an unstable Dp-brane with background fluid of fundamental strings.