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    Duality in strongly interacting systems: N = 2SUSY Yang-Mills and the quantum Hall effect


    Dolan, Brian P. (2011) Duality in strongly interacting systems: N = 2SUSY Yang-Mills and the quantum Hall effect. Fortschritte der Physik, 59 (11-12). pp. 1174-1186. ISSN 0015-8208

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    Abstract

    Classical solutions of the vacuum Maxwell’s equations exhibit a SO(2) duality symmetry, which is enhanced to Sl(2,R) when dilaton and axion fields are included. Quantum effects break this symmetry but semi-classically Sl(2, Z) symmetry, or a sub-group thereof, survives in Dirac-Schwinger-Zwanziger quantisation. Even this symmetry is expected to be broken in the full theory of quantum electrodynamics, but a modular sub-group survives as an infinite discrete symmetry of the vacua of N = 2 supersymmetric Yang- Mills theory. An analogous situation occurs in the quantum Hall effect, where different quantum Hall states are related by a modular symmetry which is a sub-group of Sl(2, Z). The similarities between the quantum Hall effect and supersymmetric Yang-Mills are reviewed and a possible link via the gauge/gravity correspondence is described. Scaling exponents in the quantum Hall effect are derived using the gauge-gravity correspondence.

    Item Type: Article
    Additional Information: This is the postprint version of the following article: Duality in strongly interacting systems: N = 2SUSY Yang-Mills and the quantum Hall effect, Brian P. Dolan, Fortschritte der Physik, 59, 11-12 Copyright © 2011 WILEY-VCH, which has been published in final form at DOI: 10.1002/prop.201100055. Invited talk at the "Fields and Strings: Theory - Cosmology - Phenomenology" session of the 10th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, 2010.
    Keywords: Duality; supersymmetric Yang-Mills; quantum Hall effect; modular symmetry; gauge-gravity correspondence;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 5987
    Identification Number: https://doi.org/10.1002/prop.201100055
    Depositing User: Dr. Brian Dolan
    Date Deposited: 25 Mar 2015 17:06
    Journal or Publication Title: Fortschritte der Physik
    Publisher: Wiley-VCH Verlag
    Refereed: Yes
    URI:

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