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A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids

A. D. Speliotopoulos
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Abstract

The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is studied and links to string theory are made. It is shown that both I_{RR} and the Polyakov string action I_{Pol} can be constructed with the same field X^mu. Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum field theory. Using generators of classical Lie algebras, I_{RR} 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 H^1(M,R^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 R^3, and in higher dimensions they reduce to the Maurer-Cartan equations for so(m).

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A. D. Speliotopoulos. 2002-08-28. A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids. https://doi.org/10.1088/0305-4470%2F35%2F41%2F316

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