N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect
Dolan, Brian P. (2006) N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect. International Journal of Modern Physics A, 21 (23/24). pp. 4807-4822. ISSN 0217-751X
It is argued that there are strong similarities between the infra-red physics of N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both systems exhibit a hierarchy of vacua with a sub-group of the modular group mapping between them. The coupling flow for pure SU(2) N = 2 supersymmetric Yang-Mills in 4-dimensions is reexamined and an earlier suggestion in the literature, that was singular at strong coupling, is modified to a form that is well behaved at both weak and strong coupling and describes the crossover in an analytic fashion. Similarities between the phase diagram and the flow of SUSY Yang-Mills and that of the quantum Hall effect are then described, with the Hall conductivity in the latter playing the role of the θ- parameter in the former. Hall plateaux, with odd denominator filling fractions, are analogous to fixed points at strong coupling in N=2 SUSY Yang-Mills, where the massless degrees of freedom carry an odd monopole charge.
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