Dark Solitons, D-branes and Noncommutative Tachyon Field Theory

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.

36 pages, 4 figures; V2: some updates in Sec.2 and Sec.4; V3: published version, typos corrected

References in corpus (8)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Observation of attraction between dark solitons
• Higgs Bundles, Gauge Theories and Quantum Groups
• Analogues of D-branes in Bose-Einstein condensates
• Vortex-boson duality in four space-time dimensions
• Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions
• Vortex lines attached to dark solitons in Bose-Einstein condensates and Boson-Vortex Duality in 3+1 Dimensions
• Strings and vortex rings

Cited by in corpus (1)

• Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models