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Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect

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dc.contributor.author Dolan, B.P.
dc.date.accessioned 2019-02-16T08:25:44Z
dc.date.available 2019-02-16T08:25:44Z
dc.date.issued 2007
dc.identifier.citation Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect / B.P. Dolan // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 119 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2000 Mathematics Subject Classification: 11F11; 81R05; 81T60; 81V70
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147800
dc.description.abstract The parallel rôles of modular symmetry in N = 2 supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills 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 Yang-Mills 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. Infra-red fixed points at strong coupling correspond to θ-vacua with θ a rational number that, in the case of pure SUSY Yang-Mills, 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 infra-red 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. uk_UA
dc.description.sponsorship This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). It is a pleasure to thank my long-term collaborator Clif f Burgess for many useful discussions on the quantum Hall ef fect. This work was partly supported by Enterprise Ireland Basic Research grant SC/2003/415. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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