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The $θ$ vacuum reveals itself as the fundamental theory of the quantum Hall effect. I. Confronting controversies

A. M. M. Pruisken·M. A. Baranov·M. Voropaev
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Abstract

The $θ$ dependence of the Grassmannian $U(m+n)/U(m)\times U(n)$ non-linear $σ$ model is reexamined. This general theory provides an important laboratory for studying the quantum Hall effect, in the special limit $m=n=0$ (replica limit). We discover however that the quantum Hall effect is in fact independent of this limit and exists as a generic topological feature of the theory for all non-negative values of $m$ and $n$. The results are in concflict with many of the historical ideas and expectations on the basis of the large $N$ expansion of the $CP^{N-1}$ or $SU(N)/U(N-1)$ model

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A. M. M. Pruisken, M. A. Baranov, M. Voropaev. 2002-06-01. The $θ$ vacuum reveals itself as the fundamental theory of the quantum Hall effect. I. Confronting controversies. https://arxiv.org/abs/cond-mat/0206011

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