Dolan, Brian P.
N=2 Supersymmetric Yang-Mills and the
Quantum Hall Effect.
International Journal of Modern Physics A, 21 (23/24).
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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