6D fractional quantum Hall effect
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Publication:1651153
DOI10.1007/JHEP05(2018)120zbMATH Open1391.58011arXiv1708.02250WikidataQ129788349 ScholiaQ129788349MaRDI QIDQ1651153
Author name not available (Why is that?)
Publication date: 11 July 2018
Published in: (Search for Journal in Brave)
Abstract: We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10+2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.
Full work available at URL: https://arxiv.org/abs/1708.02250
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