A D Speliotopoulos 2002 J. Phys. A: Math. Gen. 35 8859 doi:10.1088/0305-4470/35/41/316
A topological string: the Rasetti–Regge Lagrangian, topological quantum field theory and vortices in quantum fluids
A D Speliotopoulos1
Show affiliationsThe kinetic part of the Rasetti–Regge action IRR for vortex lines is studied and its relevance to string theory is established. It is shown that both IRR and the Polyakov string action IPol can be constructed with the same field Xμ. Unlike ING, however, IRR describes a Schwarz-type topological quantum field theory. Using generators of classical Lie algebras, IRR is generalized to higher dimensions. In all dimensions, the momentum 1-form P constructed from the canonical momentum for the vortex belongs to the first cohomology class H1(M, 
m) of the worldsheet M swept out by the vortex line. The dynamics of the vortex line thus depend directly on the topology of M. For a vortex ring, the equations of motion reduce to the Serret–Frenet equations in 3, and in higher dimensions they reduce to the Maurer–Cartan equations for so(m).
- PACS
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03.70.+k Theory of quantized fields
- MSC
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16Sxx Rings and algebras arising under various constructions
81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)
- Subjects
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Quantum gases, liquids and solids
- Dates
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Issue 41 (18 October 2002)
Received 18 June 2002
Published 1 October 2002
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A topological string: the Rasetti–Regge Lagrangian, topological quantum field theory and vortices in quantum fluids
A D Speliotopoulos 2002 J. Phys. A: Math. Gen. 35 8859
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