Abstract
We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.M. Polyakov, Fermi-Bose Transmutations Induced by Gauge Fields, Mod. Phys. Lett. A 3 (1988) 325 [INSPIRE].
N. Shaji, R. Shankar and M. Sivakumar, On Bose-fermi Equivalence in a U(1) Gauge Theory With Chern-Simons Action, Mod. Phys. Lett. A 5 (1990) 593 [INSPIRE].
E.H. Fradkin and F.A. Schaposnik, The fermion-boson mapping in three-dimensional quantum field theory, Phys. Lett. B 338 (1994) 253 [hep-th/9407182] [INSPIRE].
W. Chen, M.P.A. Fisher and Y.-S. Wu, Mott transition in an anyon gas, Phys. Rev. B 48 (1993) 13749 [cond-mat/9301037] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
S. Giombi, S. Minwalla, S. Prakash, S.P. Trivedi, S.R. Wadia and X. Yin, Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].
N. Seiberg, T. Senthil, C. Wang and E. Witten, A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics, Annals Phys. 374 (2016) 395 [arXiv:1606.01989] [INSPIRE].
J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].
J.-Y. Chen, J.H. Son, C. Wang and S. Raghu, Exact Boson-Fermion Duality on a 3D Euclidean Lattice, Phys. Rev. Lett. 120 (2018) 016602 [arXiv:1705.05841] [INSPIRE].
A. Karch, B. Robinson and D. Tong, More Abelian Dualities in 2 + 1 Dimensions, JHEP 01 (2017) 017 [arXiv:1609.04012] [INSPIRE].
D. Gaiotto, Boundaries, interfaces and dualities, talk at Natifest, Princeton, September 2016.
M. Atiyah, R. Bott and V.K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973) 279.
W. Müller, Eta invariants and manifolds with boundary, J. Diff. Geom. 40 (1994) 311.
N. Seiberg and E. Witten, Gapped Boundary Phases of Topological Insulators via Weak Coupling, PTEP 2016 (2016) 12C101 [arXiv:1602.04251] [INSPIRE].
M.A. Metlitski, S-duality of u(1) gauge theory with θ = π on non-orientable manifolds: Applications to topological insulators and superconductors, arXiv:1510.05663 [INSPIRE].
C. Csáki, C. Grojean, J. Hubisz, Y. Shirman and J. Terning, Fermions on an interval: Quark and lepton masses without a Higgs, Phys. Rev. D 70 (2004) 015012 [hep-ph/0310355] [INSPIRE].
E.H. Fradkin, Field Theories of Condensed Matter Physics, Front. Phys. 82 (2013) 1 [INSPIRE].
D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].
C.G. Callan Jr. and J.A. Harvey, Anomalies and Fermion Zero Modes on Strings and Domain Walls, Nucl. Phys. B 250 (1985) 427 [INSPIRE].
P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CF T d, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].
P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].
D.T. Son, Is the Composite Fermion a Dirac Particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].
M.A. Metlitski and A. Vishwanath, Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators, Phys. Rev. B 93 (2016) 245151 [arXiv:1505.05142] [INSPIRE].
C. Wang and T. Senthil, Dual Dirac Liquid on the Surface of the Electron Topological Insulator, Phys. Rev. X 5 (2015) 041031 [arXiv:1505.05141] [INSPIRE].
M.F.L. Golterman, K. Jansen and D.B. Kaplan, Chern-Simons currents and chiral fermions on the lattice, Phys. Lett. B 301 (1993) 219 [hep-lat/9209003] [INSPIRE].
K. Jansen and M. Schmaltz, Critical momenta of lattice chiral fermions, Phys. Lett. B 296 (1992) 374 [hep-lat/9209002] [INSPIRE].
Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [INSPIRE].
S. Sint, On the Schrödinger functional in QCD, Nucl. Phys. B 421 (1994) 135 [hep-lat/9312079] [INSPIRE].
C. Wang and T. Senthil, Half-filled Landau level, topological insulator surfaces and three-dimensional quantum spin liquids, Phys. Rev. B 93 (2016) 085110 [arXiv:1507.08290] [INSPIRE].
D.F. Mross, J. Alicea and O.I. Motrunich, Symmetry and duality in bosonization of two-dimensional Dirac fermions, Phys. Rev. X 7 (2017) 041016 [arXiv:1705.01106] [INSPIRE].
D.F. Mross, J. Alicea and O.I. Motrunich, Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2 + 1) dimensions, Phys. Rev. Lett. 117 (2016) 016802 [arXiv:1510.08455] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1712.02801
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Aitken, K., Baumgartner, A., Karch, A. et al. 3d Abelian dualities with boundaries. J. High Energ. Phys. 2018, 53 (2018). https://doi.org/10.1007/JHEP03(2018)053
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)053