Dolan, Brian P. (2006) Modular Symmetry and Fractional Charges in N = 2 Supersymmetric YangMills and the Quantum Hall Effect. Symmetry, Integrability and Geometry: Methods and Applications. ISSN 18150659

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Abstract
The parallel rôles of modular symmetry in N = 2 supersymmetric YangMills and in the quantum Hall effect are reviewed. In supersymmetric YangMills theories modular symmetry emerges as a version of Dirac’s electric – magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of N = 2 supersymmetric YangMills in 3+1 dimensions, scaling functions can be defined which are modular forms of a subgroup of the full modular group and which interpolate between vacua. Infrared fixed points at strong coupling correspond to θvacua with θ a rational number that, in the case of pure SUSY YangMills, has odd denominator. There is a mass gap for electrically charged particles which can carry fractional electric charge. A similar structure applies to the 2+1 dimensional quantum Hall effect where the hierarchy of Hall plateaux can be understood in terms of an action of the modular group and the stability of Hall plateaux is due to the fact that odd denominator Hall conductivities are attractive infrared fixed points. There is a mass gap for electrically charged excitations which, in the case of the fractional quantum Hall effect, carry fractional electric charge.
Item Type:  Article 

Uncontrolled Keywords:  duality, modular symmetry, supersymmetry, quantum Hall effect 
Divisions:  School of Theoretical Physics > Preprints 
Date Deposited:  05 Oct 2017 19:31 
Last Modified:  16 Jul 2018 10:31 
URI:  http://dair.dias.ie/id/eprint/179 
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