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
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: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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