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    Super universality of the quantum Hall effect and the "large NN picture" of the Ï‘\vartheta angle

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    It is shown that the "massless chiral edge excitations" are an integral and universal aspect of the low energy dynamics of the ϑ\vartheta vacuum that has historically gone unnoticed. Within the SU(M+N)/S(U(M)×U(N))SU(M+N)/S(U(M) \times U(N)) non-linear sigma model we introduce an effective theory of "edge excitations" that fundamentally explains the quantum Hall effect. In sharp contrast to the common beliefs in the field our results indicate that this macroscopic quantization phenomenon is, in fact, a {\em super universal} strong coupling feature of the ϑ\vartheta angle with the replica limit M=N=0M=N=0 only playing a role of secondary importance. To demonstrate super universality we revisit the large NN expansion of the CPN−1CP^{N-1} model. We obtain, for the first time, explicit scaling results for the quantum Hall effect including quantum criticality of the quantum Hall plateau transition. Consequently a scaling diagram is obtained describing the cross-over between the weak coupling "instanton phase" and the strong coupling "quantum Hall phase" of the large NN theory. Our results are in accordance with the "instanton picture" of the ϑ\vartheta angle but fundamentally invalidate all the ideas, expectations and conjectures that are based on the historical "large NN picture."Comment: 40 pages, 9 figure
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