Duality in Supersymmetric Yang-Mills and the Quantum Hall effect

Dolan, Brian P. (2006) Duality in Supersymmetric Yang-Mills and the Quantum Hall effect. (Preprint)

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It is shown that the long-wavelength, zero-frequency limits of N = 2 supersymmetric Yang-Mills in 3 + 1-dimensions and the quantum Hall effect in 2 + 1 dimensions have many features in common. The phases of both these systems have a hierarchical structure which can be organised and understood in terms of a specific sub-group of the modular group acting on a complex parameter. The complex coupling has positive imaginary part which is the Yang-Mills coupling in the former case and the Ohmic conductivity in the latter. In both case the real part of the complex parameter is associated with a topological term in the effective action for the respective theory. The theoretical scaling flow of SUSY Yang-Mills that follows from modular symmetry is given by a modular form and shows a remarkable similarity to the experimental scaling flow of the quantum Hall effect which, though not necessarily associated with modular forms, is nevertheless strongly constrained by modular symmetry.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:46
Last Modified: 14 Dec 2022 20:30
URI: https://dair.dias.ie/id/eprint/485

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