A Duality Web in 2+1 Dimensions and Condensed Matter Physics
By N. Seiberg, T. Senthil, Chong Wang, E. Witten. 2016
480 citations recorded by the source corpus.
Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in $2+1$ 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 $2+1$-dimensional analog of QED with a single Dirac fermion (a theory known as $U(1)_{1/2}$) is identified with the $O(2)$ 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 $3+1$-dimensional $S$-duality.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/f68bfcab5db8393c13ab17c749d8e84b736a4f33
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Particle-Vortex Duality from 3D Bosonization (2016, background): “This change of quantization can be accomplished by the addition of an auxiliary gauge [47].”
- An introduction to spontaneous symmetry breaking (2019, background): “Recently, the approach has been extended to systems involving multiple species of particles including fermions, in a so-called “web of dualities” [87,88].”
- Chern-Simons-matter dualities with SO and USp gauge groups (2016, background): “The very same two theories, viewed as U(1) theories, are also mapped to each other by the U(1) duality of [26,28,27].”
- Anomalies in the space of coupling constants and their dynamical applications II (2019, unknown): “This idea has been fruitfully applied in the study of 3d dualities by tracking the total discontinuity in various Chern-Simons levels for background fields as a parameter is varied [11–22].”
- Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “Appendix C of [33], Appendix B of [34], and also [6].”
- Particle-vortex duality in topological insulators and superconductors (2016, methodology): “We would like to thank David Tong and Edward Witten for encouraging us to complete this work as soon as we did.”
- Comments on global symmetries, anomalies, and duality in (2 + 1)d (2017, methodology): “The second duality maps an interacting bosonic theory to a free fermion [38].”