One-dimensional string theory with vortices as the upside down matrix oscillator
Aug, 199148 pages
Published in:
- Int.J.Mod.Phys.A 8 (1993) 809-852
e-Print:
- hep-th/0012228 [hep-th]
Report number:
- LPTENS-91-24,
- KUNS-1094,
- KUNS-1094-HE(TH)-91-14
Citations per year
Abstract:
We study matrix quantum mechanics at a finite temperature equivalent to one dimensional compactified string theory with vortex (winding) excitations. It is explicitly demonstrated that the states transforming under non-trivial U(N) representations describe various configurations vortices and anti-vortices. For example, for the adjoint representation the Feynman graphs (representing discretized world-sheets) contain two faces with the boundaries wrapping around the compactified target space which is equivalent to a vortex-anti-vortex pair. A technique is developed to calculate partition functions in a given representation for the standard matrix oscillator. It enables us to obtain the partition function in the presence of a vortex-anti-vortex pair in the double scaling limit using an analytical continuation to the upside-down oscillator. The Berezinski-Kosterlitz-Thouless phase transition occurs in a similar way and at the same temperature as in the flat 2D space. A possible generalization of our technique to any dimension of the embedding space is discussed.Note:
- 51 pages, 7 figures, revised version of a 1991 paper
- quantum mechanics
- matrix model
- dimension: 1
- string model
- partition function
- vortex
- scaling
- boundary condition
- finite temperature
- critical phenomena
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