Hyperelliptic curves for multi-channel quantum wires and the multi-channel Kondo problem

Abstract

We study the current in a multi-channel quantum wire and the magnetization in the multi-channel Kondo problem. We show that at zero temperature they can be written simply in terms of contour integrals over a (two-dimensional) hyperelliptic curve. This allows one to easily demonstrate the existence of weak-coupling to strong-coupling dualities. In the Kondo problem, the curve is the same for under- and over-screened cases; the only change is in the contour.

7 pages, 1 figure, revtex

References in corpus (5)

• Coulomb Interactions and Mesoscopic Effects in Carbon Nanotubes
• Perturbation of infra-red fixed points and duality in quantum impurity problems
• Self-duality in quantum impurity problems
• Tunneling in quantum wires I: Exact solution of the spin isotropic case
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• Potts model: Duality, Uniformization and the Seiberg-Witten modulus
• Differential equations and duality in massless integrable field theories at zero temperature