A duality web in 2 + 1 dimensions and condensed matter physics
Abstract
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 consistencymore »
- Authors:
-
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Harvard Univ., Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Institute for Advanced Study, Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1533508
- Alternate Identifier(s):
- OSTI ID: 1398567
- Grant/Contract Number:
- SC0009988; DMR-1305741; PHY-1314311
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Annals of Physics
- Additional Journal Information:
- Journal Volume: 374; Journal Issue: C; Journal ID: ISSN 0003-4916
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Field theory duality; Quantum hall effect; Topological insulator; Composite fermions; Quantum criticality
Citation Formats
Seiberg, Nathan, Senthil, T., Wang, Chong, and Witten, Edward. A duality web in 2 + 1 dimensions and condensed matter physics. United States: N. p., 2016.
Web. doi:10.1016/j.aop.2016.08.007.
Seiberg, Nathan, Senthil, T., Wang, Chong, & Witten, Edward. A duality web in 2 + 1 dimensions and condensed matter physics. United States. https://doi.org/10.1016/j.aop.2016.08.007
Seiberg, Nathan, Senthil, T., Wang, Chong, and Witten, Edward. Tue .
"A duality web in 2 + 1 dimensions and condensed matter physics". United States. https://doi.org/10.1016/j.aop.2016.08.007. https://www.osti.gov/servlets/purl/1533508.
@article{osti_1533508,
title = {A duality web in 2 + 1 dimensions and condensed matter physics},
author = {Seiberg, Nathan and Senthil, T. and Wang, Chong and Witten, Edward},
abstractNote = {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.},
doi = {10.1016/j.aop.2016.08.007},
journal = {Annals of Physics},
number = C,
volume = 374,
place = {United States},
year = {Tue Aug 16 00:00:00 EDT 2016},
month = {Tue Aug 16 00:00:00 EDT 2016}
}
Web of Science
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