Skip to main content

3d Abelian dualities with boundaries

A preprint version of the article is available at arXiv.

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.

References

  1. A.M. Polyakov, Fermi-Bose Transmutations Induced by Gauge Fields, Mod. Phys. Lett. A 3 (1988) 325 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  2. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. 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].

  5. 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].

  6. 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].

    ADS  Article  Google Scholar 

  7. O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  8. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  9. A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].

    Article  Google Scholar 

  10. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  11. J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. 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].

    ADS  Article  Google Scholar 

  13. A. Karch, B. Robinson and D. Tong, More Abelian Dualities in 2 + 1 Dimensions, JHEP 01 (2017) 017 [arXiv:1609.04012] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  14. D. Gaiotto, Boundaries, interfaces and dualities, talk at Natifest, Princeton, September 2016.

  15. M. Atiyah, R. Bott and V.K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973) 279.

    ADS  MathSciNet  Article  MATH  Google Scholar 

  16. W. Müller, Eta invariants and manifolds with boundary, J. Diff. Geom. 40 (1994) 311.

    MathSciNet  Article  MATH  Google Scholar 

  17. N. Seiberg and E. Witten, Gapped Boundary Phases of Topological Insulators via Weak Coupling, PTEP 2016 (2016) 12C101 [arXiv:1602.04251] [INSPIRE].

  18. 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].

  19. 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].

  20. E.H. Fradkin, Field Theories of Condensed Matter Physics, Front. Phys. 82 (2013) 1 [INSPIRE].

    MATH  Google Scholar 

  21. D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].

  22. 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].

    ADS  MathSciNet  Article  Google Scholar 

  23. 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].

    ADS  Article  MATH  Google Scholar 

  24. P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  25. D.T. Son, Is the Composite Fermion a Dirac Particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].

    Article  Google Scholar 

  26. 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].

    ADS  Article  Google Scholar 

  27. 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].

    Article  Google Scholar 

  28. 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].

  29. K. Jansen and M. Schmaltz, Critical momenta of lattice chiral fermions, Phys. Lett. B 296 (1992) 374 [hep-lat/9209002] [INSPIRE].

  30. Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [INSPIRE].

  31. S. Sint, On the Schrödinger functional in QCD, Nucl. Phys. B 421 (1994) 135 [hep-lat/9312079] [INSPIRE].

  32. 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].

    ADS  Article  Google Scholar 

  33. 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].

    Article  Google Scholar 

  34. 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].

    ADS  Article  Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to Kyle Aitken.

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/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP03(2018)053

Keywords

  • Chern-Simons Theories
  • Duality in Gauge Field Theories
  • Field Theories in Lower Dimensions
  • Anomalies in Field and String Theories