Dark Solitons, D-branes and Noncommutative Tachyon Field Theory

TL;DR

This paper explores the duality between boson/vortex systems and string theory, revealing how solitons in noncommutative tachyon fields correspond to D-branes, bridging condensed matter and string theory insights.

Contribution

It introduces a novel mapping between the Gross-Pitaevskii theory and effective string theory, establishing a connection with noncommutative tachyon fields and D-branes.

Findings

Seiberg-Witten map between commutative and noncommutative tachyon theories

Identification of solitons with D-branes in the effective string framework

Validation of the duality and soliton correspondence through various checks

Abstract

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.