  In this paper we discuss the boson/vortex duality by mapping the (3+1)D
Gross-Pitaevskii theory into an effective string theory in the presence of
boundaries. Via the effective string theory, we find the Seiberg-Witten map
between the commutative and the noncommutative tachyon field theories, and
consequently identify their soliton solutions with $D$-branes in the effective
string theory. We perform various checks of the duality map and the
identification of soliton solutions. This new insight between the
Gross-Pitaevskii theory and the effective string theory explains the similarity
of these two systems at quantitative level.
