Advertisement

Journal of High Energy Physics

, 2018:123 | Cite as

Dark monopoles and SL(2, ℤ) duality

  • John TerningEmail author
  • Christopher B. Verhaaren
Open Access
Regular Article - Theoretical Physics

Abstract

We explore kinetic mixing between two Abelian gauge theories that have both electric and magnetic charges. When one of the photons becomes massive, novel effects arise in the low-energy effective theory, including the failure of Dirac charge quantization as particles from one sector obtain parametrically small couplings to the photon of the other. We maintain a manifest SL(2, ℤ) duality throughout our analysis, which is the diagonal subgroup of the dualities of the two un-mixed gauge theories.

Keywords

Duality in Gauge Field Theories Solitons Monopoles and Instantons Spontaneous Symmetry Breaking 

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. Hook and J. Huang, Bounding millimagnetically charged particles with magnetars, Phys. Rev. D 96 (2017) 055010 [arXiv:1705.01107] [INSPIRE].ADSGoogle Scholar
  2. [2]
    B. Holdom, Two U(1)’s and Epsilon Charge Shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    F. Brummer and J. Jaeckel, Minicharges and Magnetic Monopoles, Phys. Lett. B 675 (2009) 360 [arXiv:0902.3615] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    F. Brummer, J. Jaeckel and V.V. Khoze, Magnetic Mixing: Electric Minicharges from Magnetic Monopoles, JHEP 06 (2009) 037 [arXiv:0905.0633] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    C. Gomez Sanchez and B. Holdom, Monopoles, strings and dark matter, Phys. Rev. D 83 (2011) 123524 [arXiv:1103.1632] [INSPIRE].ADSGoogle Scholar
  6. [6]
    P.A.M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A 133 (1931) 60 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  7. [7]
    J.S. Schwinger, Magnetic charge and quantum field theory, Phys. Rev. 144 (1966) 1087 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    J.S. Schwinger, Sources and magnetic charge, Phys. Rev. 173 (1968) 1536 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    J.S. Schwinger, Magnetic Charge and the Charge Quantization Condition, Phys. Rev. D 12 (1975) 3105 [INSPIRE].ADSGoogle Scholar
  10. [10]
    D. Zwanziger, Quantum field theory of particles with both electric and magnetic charges, Phys. Rev. 176 (1968) 1489 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    P.A.M. Dirac, The theory of magnetic poles, Phys. Rev. 74 (1948) 817 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    C.R. Hagen, Noncovariance of the Dirac Monopole, Phys. Rev. 140 (1965) B804 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    D. Zwanziger, Local Lagrangian quantum field theory of electric and magnetic charges, Phys. Rev. D 3 (1971) 880 [INSPIRE].ADSMathSciNetGoogle Scholar
  14. [14]
    R.A. Brandt and F. Neri, Remarks on Zwanzigers Local Quantum Field Theory of Electric and Magnetic Charge, Phys. Rev. D 18 (1978) 2080 [INSPIRE].ADSGoogle Scholar
  15. [15]
    R.A. Brandt, F. Neri and D. Zwanziger, Lorentz Invariance of the Quantum Field Theory of Electric and Magnetic Charge, Phys. Rev. Lett. 40 (1978) 147 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    R.A. Brandt, F. Neri and D. Zwanziger, Lorentz Invariance From Classical Particle Paths in Quantum Field Theory of Electric and Magnetic Charge, Phys. Rev. D 19 (1979) 1153 [INSPIRE].ADSMathSciNetGoogle Scholar
  17. [17]
    C. Csáki, Y. Shirman and J. Terning, Anomaly Constraints on Monopoles and Dyons, Phys. Rev. D 81 (2010) 125028 [arXiv:1003.0448] [INSPIRE].ADSMathSciNetGoogle Scholar
  18. [18]
    J.L. Cardy and E. Rabinovici, Phase Structure of Z(p) Models in the Presence of a Theta Parameter, Nucl. Phys. B 205 (1982) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J.L. Cardy, Duality and the Theta Parameter in Abelian Lattice Models, Nucl. Phys. B 205 (1982) 17 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    A.D. Shapere and F. Wilczek, Selfdual Models with Theta Terms, Nucl. Phys. B 320 (1989) 669 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    C. Vafa and E. Witten, A strong coupling test of S duality, Nucl. Phys. B 431 (1994) 3 [hep-th/9408074] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    E. Witten, On S duality in Abelian gauge theory, Selecta Math. 1 (1995) 383 [hep-th/9505186] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    E.P. Verlinde, Global aspects of electric-magnetic duality, Nucl. Phys. B 455 (1995) 211 [hep-th/9506011] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Y. Lozano, S duality in gauge theories as a canonical transformation, Phys. Lett. B 364 (1995) 19 [hep-th/9508021] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    A.A. Kehagias, A canonical approach to s duality in Abelian gauge theory, hep-th/9508159 [INSPIRE].
  26. [26]
    A. Strominger, Magnetic Corrections to the Soft Photon Theorem, Phys. Rev. Lett. 116 (2016) 031602 [arXiv:1509.00543] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    L.V. Laperashvili and H.B. Nielsen, Dirac relation and renormalization group equations for electric and magnetic fine structure constants, Mod. Phys. Lett. A 14 (1999) 2797 [hep-th/9910101] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    K. Colwell and J. Terning, S-duality and Helicity Amplitudes, JHEP 03 (2016) 068 [arXiv:1510.07627] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    J.H. Schwarz and A. Sen, Duality symmetric actions, Nucl. Phys. B 411 (1994) 35 [hep-th/9304154] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    J. Terning and C.B. Verhaaren, Resolving the Weinberg Paradox with Topology, arXiv:1809.05102 [INSPIRE].
  31. [31]
    E. Witten, Dyons of Charge eθ/2π, Phys. Lett. B 86 (1979) 283 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    G. ’t Hooft, Magnetic Monopoles in Unified Gauge Theories, Nucl. Phys. B 79 (1974) 276 [INSPIRE].
  33. [33]
    A.M. Polyakov, Particle Spectrum in the Quantum Field Theory, JETP Lett. 20 (1974) 194 [Pisma Zh. Eksp. Teor. Fiz. 20 (1974) 430] [INSPIRE].
  34. [34]
    P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    S.R. Coleman, The Magnetic Monopole Fifty Years Later, HUTP-82-A032 [INSPIRE].
  36. [36]
    Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115 (1959) 485 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [INSPIRE].
  38. [38]
    N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    C.G. Callan Jr., Dyon-Fermion Dynamics, Phys. Rev. D 26 (1982) 2058 [INSPIRE].ADSGoogle Scholar
  40. [40]
    J.A. Harvey, Magnetic Monopoles With Fractional Charges, Phys. Lett. B 131 (1983) 104 [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A.J. Niemi, M.B. Paranjape and G.W. Semenoff, On the Electric Charge of the Magnetic Monopole, Phys. Rev. Lett. 53 (1984) 515 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    A.S. Goldhaber, Role of Spin in the Monopole Problem, Phys. Rev. 140 (1965) B1407 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    J.J. Thomson, On Momentum in the Electric Field, Philos. Mag. 8 (1904) 331.CrossRefzbMATHGoogle Scholar
  44. [44]
    G. ’t Hooft, Gauge Fields with Unified Weak, Electromagnetic, and Strong Interactions, talk given at EPS International Conference on High Energy Physics, Palermo, Italy, June 23–28, 1975, published in High Energy Physics, A. Zichichi ed., Editrice Compositori, Bologna, Italy, (1976).Google Scholar
  45. [45]
    S. Mandelstam, Vortices and Quark Confinement in Nonabelian Gauge Theories, Phys. Rept. 23 (1976) 245 [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    S. Mandelstam, Charge-Monopole Duality and the Phases of Nonabelian Gauge Theories, Phys. Rev. D 19 (1979) 2391 [INSPIRE].ADSGoogle Scholar
  47. [47]
    H.B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    R. Acharya and Z. Horvath, Taylors nonclassical theory of magnetic monopoles as a spontaneously broken UL1 × UR1 model, Lett. Nuovo Cim. 8S2 (1973) 513 [INSPIRE].
  49. [49]
    M. Creutz, The Higgs Mechanism and Quark Confinement, Phys. Rev. D 10 (1974) 2696 [INSPIRE].ADSGoogle Scholar
  50. [50]
    A. Jevicki and P. Senjanovic, String-Like Solution of Higgs Model with Magnetic Monopoles, Phys. Rev. D 11 (1975) 860 [INSPIRE].ADSGoogle Scholar
  51. [51]
    A.P. Balachandran, H. Rupertsberger and J. Schechter, Monopole Theories with Massless and Massive Gauge Fields, Phys. Rev. D 11 (1975) 2260 [INSPIRE].ADSGoogle Scholar
  52. [52]
    F.V. Gubarev, M.I. Polikarpov and V.I. Zakharov, Monopole-anti-monopole interaction in Abelian Higgs model, Phys. Lett. B 438 (1998) 147 [hep-th/9805175] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    S. Weinberg, Photons and gravitons in perturbation theory: Derivation of Maxwells and Einsteins equations, Phys. Rev. 138 (1965) B988 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    Y. Nambu, String-Like Configurations in the Weinberg-Salam Theory, Nucl. Phys. B 130 (1977) 505 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Center for Quantum Mathematics and Physics (QMAP), Department of PhysicsUniversity of CaliforniaDavisU.S.A.

Personalised recommendations