A duality web in \(2+1\) dimensions and condensed matter physics
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Publication:1692600
DOI10.1016/J.AOP.2016.08.007zbMATH Open1377.81262arXiv1606.01989OpenAlexW2414926551MaRDI QIDQ1692600
Author name not available (Why is that?)
Publication date: 10 January 2018
Published in: (Search for Journal in Brave)
Abstract: Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the -dimensional analog of QED with a single Dirac fermion (a theory known as ) is identified with the Wilson-Fisher fixed point. The gauged version of that fixed point with a Chern-Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped boundary states) and the problem of electrons in the lowest Landau level at half filling. (Our techniques also clarify some points in the fractional Hall effect and its description using flux attachment.) In addition to presenting several consistency checks, we also present plausible (but not rigorous) derivations of the dualities and relate them to -dimensional -duality.
Full work available at URL: https://arxiv.org/abs/1606.01989
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