Advertisement

3d Abelian dualities with boundaries

  • Kyle AitkenEmail author
  • Andrew Baumgartner
  • Andreas Karch
  • Brandon Robinson
Open Access
Regular Article - Theoretical Physics
First Online:

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.

Keywords

Chern-Simons Theories Duality in Gauge Field Theories Field Theories in Lower Dimensions Anomalies in Field and String Theories 
Download to read the full article text

Notes

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.

References

  1. [1]
    A.M. Polyakov, Fermi-Bose Transmutations Induced by Gauge Fields, Mod. Phys. Lett. A 3 (1988) 325 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [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. [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. [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].ADSCrossRefGoogle Scholar
  7. [7]
    O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    A. Karch and D. Tong, Particle-Vortex Duality from 3d Bosonization, Phys. Rev. X 6 (2016) 031043 [arXiv:1606.01893] [INSPIRE].CrossRefGoogle Scholar
  10. [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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J. Murugan and H. Nastase, Particle-vortex duality in topological insulators and superconductors, JHEP 05 (2017) 159 [arXiv:1606.01912] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [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].ADSCrossRefGoogle Scholar
  13. [13]
    A. Karch, B. Robinson and D. Tong, More Abelian Dualities in 2 + 1 Dimensions, JHEP 01 (2017) 017 [arXiv:1609.04012] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    D. Gaiotto, Boundaries, interfaces and dualities, talk at Natifest, Princeton, September 2016.Google Scholar
  15. [15]
    M. Atiyah, R. Bott and V.K. Patodi, On the heat equation and the index theorem, Invent. Math. 19 (1973) 279.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    W. Müller, Eta invariants and manifolds with boundary, J. Diff. Geom. 40 (1994) 311.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    N. Seiberg and E. Witten, Gapped Boundary Phases of Topological Insulators via Weak Coupling, PTEP 2016 (2016) 12C101 [arXiv:1602.04251] [INSPIRE].
  18. [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. [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. [20]
    E.H. Fradkin, Field Theories of Condensed Matter Physics, Front. Phys. 82 (2013) 1 [INSPIRE].zbMATHGoogle Scholar
  21. [21]
    D.B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].
  22. [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].ADSMathSciNetCrossRefGoogle Scholar
  23. [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].ADSCrossRefzbMATHGoogle Scholar
  24. [24]
    P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    D.T. Son, Is the Composite Fermion a Dirac Particle?, Phys. Rev. X 5 (2015) 031027 [arXiv:1502.03446] [INSPIRE].CrossRefGoogle Scholar
  26. [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].ADSCrossRefGoogle Scholar
  27. [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].CrossRefGoogle Scholar
  28. [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. [29]
    K. Jansen and M. Schmaltz, Critical momenta of lattice chiral fermions, Phys. Lett. B 296 (1992) 374 [hep-lat/9209002] [INSPIRE].
  30. [30]
    Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B 406 (1993) 90 [hep-lat/9303005] [INSPIRE].
  31. [31]
    S. Sint, On the Schrödinger functional in QCD, Nucl. Phys. B 421 (1994) 135 [hep-lat/9312079] [INSPIRE].
  32. [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].ADSCrossRefGoogle Scholar
  33. [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].CrossRefGoogle Scholar
  34. [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].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Kyle Aitken
    • 1
    Email author
  • Andrew Baumgartner
    • 1
  • Andreas Karch
    • 1
  • Brandon Robinson
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of WashingtonSeattleU.S.A.
  2. 2.School of Physics and Astronomy and STAG Research CentreUniversity of SouthamptonHighfieldU.K.

Personalised recommendations