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Journal of High Energy Physics

, 2019:114 | Cite as

Defect QED: dielectric without a dielectric, monopole without a monopole

  • Gianluca Grignani
  • Gordon W. SemenoffEmail author
Open Access
Regular Article - Theoretical Physics
  • 34 Downloads

Abstract

We study a class of defect quantum field theories where the quantum field theory in the 3+1-dimensional bulk is a free photon and charged matter and the interactions of the photons with the charges occur entirely on a 2+1-dimensional defect. We observe that at the fully quantum level, the effective action of such a theory is still a defect field theory with free photons propagating in the bulk and the nonlinearities in the quantum corrections to the Maxwell equations confined to the defect. We use this observation to show that the defect field theory has interesting electromagnetic properties. The electromagnetic fields sourced by static test charges are attenuated as if the bulk surrounding them were filled with a dielectric material. This is particularly interesting when the observer and test charge are on opposite sides of the defect. Then the effect is isotropic and it is operative even in the region near the defect. If the defect is in a time reversal violating state, image charges have the appearance of electrically and magnetically charged dyons. We present the example of a single layer in a quantum Hall state. We observe that the charge screening effect in charge neutral graphene should be significant, and even more dramatic when the layer is in a metallic state with mobile electrons.

Keywords

Conformal Field Theory Field Theories in Lower Dimensions 

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]
    C.P. Herzog, K.-W. Huang, I. Shamir and J. Virrueta, Superconformal Models for Graphene and Boundary Central Charges, JHEP09 (2018) 161 [arXiv:1807.01700] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    C.P. Herzog and K.-W. Huang, Boundary Conformal Field Theory and a Boundary Central Charge, JHEP10 (2017) 189 [arXiv:1707.06224] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    D. Dudal, A.J. Mizher and P. Pais, Exact quantum scale invariance of three-dimensional reduced QED theories, Phys. Rev.D 99 (2019) 045017 [arXiv:1808.04709] [INSPIRE].
  4. [4]
    L. Di Pietro, D. Gaiotto, E. Lauria and J. Wu, 3d Abelian Gauge Theories at the Boundary, JHEP05 (2019) 091 [arXiv:1902.09567] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  5. [5]
    E. Witten, SL(2, ℤ) action on three-dimensional conformal field theories with Abelian symmetry, hep-th/0307041 [INSPIRE].
  6. [6]
    D. Gaiotto and E. Witten, Supersymmetric Boundary Conditions in N = 4 Super Yang-Mills Theory, J. Statist. Phys.135 (2009) 789 [arXiv:0804.2902] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    E.V. Gorbar, V.P. Gusynin and V.A. Miransky, Dynamical chiral symmetry breaking on a brane in reduced QED, Phys. Rev.D 64 (2001) 105028 [hep-ph/0105059] [INSPIRE].
  8. [8]
    W. Chen, G.W. Semenoff and Y.-S. Wu, Two loop analysis of nonAbelian Chern-Simons theory, Phys. Rev.D 46 (1992) 5521 [hep-th/9209005] [INSPIRE].
  9. [9]
    W. Chen, G.W. Semenoff and Y.-s. Wu, Scale and conformal invariance in Chern-Simons matter field theory, Phys. Rev.D 44 (1991) 1625 [INSPIRE].
  10. [10]
    R.D. Pisarski, Chiral Symmetry Breaking in Three-Dimensional Electrodynamics, Phys. Rev.D 29 (1984) 2423 [INSPIRE].
  11. [11]
    T.W. Appelquist, M.J. Bowick, D. Karabali and L.C.R. Wijewardhana, Spontaneous Chiral Symmetry Breaking in Three-Dimensional QED, Phys. Rev.D 33 (1986) 3704 [INSPIRE].
  12. [12]
    S. Teber, Electromagnetic current correlations in reduced quantum electrodynamics, Phys. Rev.D 86 (2012) 025005 [arXiv:1204.5664] [INSPIRE].
  13. [13]
    A.V. Kotikov and S. Teber, Note on an application of the method of uniqueness to reduced quantum electrodynamics, Phys. Rev.D 87 (2013) 087701 [arXiv:1302.3939] [INSPIRE].
  14. [14]
    S. Teber and A.V. Kotikov, Interaction corrections to the minimal conductivity of graphene via dimensional regularization, EPL107 (2014) 57001 [arXiv:1407.7501] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    S. Teber and A.V. Kotikov, The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations, Theor. Math. Phys.190 (2017) 446 [arXiv:1602.01962] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  16. [16]
    B. Basa, G. La Nave and P.W. Phillips, Classification of Non-local Actions: Area versus Volume Entanglement Entropy, arXiv:1907.09494 [INSPIRE].
  17. [17]
    G. La Nave, K. Limtragool and P.W. Phillips, Fractional Electromagnetism in Quantum Matter and High-Energy Physics, Rev. Mod. Phys.91 (2019) 021003 [arXiv:1904.01023] [INSPIRE].
  18. [18]
    G.W. Semenoff, P. Sodano and Y.-S. Wu, Renormalization of the Statistics Parameter in Three-dimensional Electrodynamics, Phys. Rev. Lett.62 (1989) 715 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S.T. Bramwell and M.J.P. Gingras, Spin Ice State in Frustrated Magnetic Pyrochlore Materials, Science294 (2001) 1495 [cond-mat/0201427].
  20. [20]
    C. Castelnovo, R. Moessner and S.L. Sondhi, Magnetic monopoles in spin ice, Nature451N7174 (2008) 42 [arXiv:0710.5515] [INSPIRE].
  21. [21]
    O. Tchernyshyov, Magnetism: Freedom for the poles, Nature451 (2008) 22.ADSCrossRefGoogle Scholar
  22. [22]
    M.J.P. Gingras, Observing Monopoles in a Magnetic Analog of Ice, Science326 (2009) 375 [arXiv:1005.3557].MathSciNetCrossRefGoogle Scholar
  23. [23]
    V. Pietila and M. Mottonen, Creation of Dirac Monopoles in Spinor Bose-Einstein Condensates, Phys. Rev. Lett.103 (2009) 030401 [arXiv:0903.4732] [INSPIRE].
  24. [24]
    M.W. Ray, E. Ruokokoski, S. Kandel, M. M¨ott¨onen and D.S. Hall, Observation of Dirac monopoles in a synthetic magnetic field, Nature505 (2014) 657 [arXiv:1408.3133] [INSPIRE].
  25. [25]
    X.-L. Qi, R. Li, J. Zang and S.-C. Zhang, Inducing a Magnetic Monopole with Topological Surface States, Science323 (2009) 1184 [arXiv:0811.1303] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    Q.N. Meier et al., Search for the magnetic monopole at a magnetoelectric surface, Phys. Rev.X 9 (2019) 011011 [arXiv:1804.07694] [INSPIRE].
  27. [27]
    W. Xi and W. Ku, Hunting down magnetic monopoles in two-dimensional topological insulators and superconductors, Phys. Rev.B 100 (2019) 121201 [arXiv:1802.05624] [INSPIRE].
  28. [28]
    A. Uri et al., Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene, arXiv:1908.02466 [INSPIRE].
  29. [29]
    G.W. Semenoff, Condensed Matter Simulation of a Three-dimensional Anomaly, Phys. Rev. Lett.53 (1984) 2449 [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    K.S. Novoselov et al., Two-dimensional gas of massless Dirac fermions in graphene, Nature438 (2005) 197 [cond-mat/0509330] [INSPIRE].
  31. [31]
    Y. Zhang, Y.-W. Tan, H.L. Stormer and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature438 (2005) 201 [cond-mat/0509355] [INSPIRE].
  32. [32]
    A.J. Niemi and G.W. Semenoff, Axial Anomaly Induced Fermion Fractionization and Effective Gauge Theory Actions in Odd Dimensional Space-Times, Phys. Rev. Lett.51 (1983) 2077 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    A.N. Redlich, Parity Violation and Gauge Noninvariance of the Effective Gauge Field Action in Three-Dimensions, Phys. Rev.D 29 (1984) 2366 [INSPIRE].
  34. [34]
    A.N. Redlich, Gauge Noninvariance and Parity Violation of Three-Dimensional Fermions, Phys. Rev. Lett.52 (1984) 18 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    X. Wu, X. Li, Z. Song, C. Berger and W.A. de Heer, Weak antilocalization in epitaxial graphene: Evidence for chiral electrons, Phys. Rev. Lett.98 (2007) 136801.ADSCrossRefGoogle Scholar
  36. [36]
    E.G. Mishchenko, Effect of Electron-Electron Interactions on the Conductivity of Clean Graphene, Phys. Rev. Lett.98 (2007) 216801.ADSCrossRefGoogle Scholar
  37. [37]
    D.E. Sheehy and J. Schmalian, Quantum Critical Scaling in Graphene, Phys. Rev. Lett.99 (2007) 226803.ADSCrossRefGoogle Scholar
  38. [38]
    V. Juricic, O. Vafek and I.F. Herbut, Conductivity of interacting massless Dirac particles in graphene: Collisionless regime, Phys. Rev.B 82 (2010) 235402 [arXiv:1009.3269] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di Fisica e GeologiaUniversità di Perugia, I.N.F.N. Sezione di PerugiaPerugiaItaly
  2. 2.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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