Journal of High Energy Physics

, 2011:112 | Cite as

Constraining noncommutative field theories with holography

Article

Abstract

An important window to quantum gravity phenomena in low energy noncom-mutative (NC) quantum field theories (QFTs) gets represented by a specific form of UV/IR mixing. Yet another important window to quantum gravity, a holography, manifests itself in effective QFTs as a distinct UV/IR connection. In matching these two principles, a useful relationship connecting the UV cutoff ΛUV, the IR cutoff ΛIR and the scale of non-commutativity ΛNC, can be obtained. We show that an effective QFT endowed with both principles may not be capable to fit disparate experimental bounds simultaneously, like the muon g − 2 and the masslessness of the photon. Also, the constraints from the muon g − 2 preclude any possibility to observe the birefringence of the vacuum coming from objects at cosmological distances. On the other hand, in NC theories without the UV completion, where the perturbative aspect of the theory (obtained by truncating a power series in \( \Lambda_{\text{NC}}^{ - 2} \)) becomes important, a heuristic estimate of the region where the perturbative expansion is well-defined ENC ≲ 1, gets affected when holography is applied by providing the energy of the system E a ΛNC-dependent lower limit. This may affect models which try to infer the scale ΛNC by using data from low-energy experiments.

Keywords

Non-Commutative Geometry Models of Quantum Gravity 

References

  1. [1]
    A. Connes, M.R. Douglas and A.S. Schwarz, Noncommutative geometry and matrix theory: Compactification on tori, JHEP 02 (1998) 003 [hep-th/9711162] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  2. [2]
    N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  3. [3]
    M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [SPIRES].CrossRefMathSciNetADSMATHGoogle Scholar
  4. [4]
    R.J. Szabo, Quantum Field Theory on Noncommutative Spaces, Phys. Rept. 378 (2003) 207 [hep-th/0109162] [SPIRES].MATHCrossRefADSGoogle Scholar
  5. [5]
    C.-S. Chu, Non-commutative geometry from strings, hep-th/0502167 [SPIRES].
  6. [6]
    S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, JHEP 02 (2000) 020 [hep-th/9912072] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    A. Matusis, L. Susskind and N. Toumbas, The IR/UV connection in the non-commutative gauge theories, JHEP 12 (2000) 002 [hep-th/0002075] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  8. [8]
    T. Filk, Divergencies in a field theory on quantum space, Phys. Lett. B 376 (1996) 53 [SPIRES].MathSciNetADSGoogle Scholar
  9. [9]
    N. Ishibashi, S. Iso, H. Kawai and Y. Kitazawa, Wilson loops in noncommutative Yang-Mills, Nucl. Phys. B 573 (2000) 573 [hep-th/9910004] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    L. Álvarez-Gaumé and M.A. Vazquez-Mozo, General properties of noncommutative field theories, Nucl. Phys. B 668 (2003) 293 [hep-th/0305093] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    J. Jaeckel, V.V. Khoze and A. Ringwald, Telltale traces of U(1) fields in noncommutative standard model extensions, JHEP 02 (2006) 028 [hep-ph/0508075] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    S.A. Abel, J. Jaeckel, V.V. Khoze and A. Ringwald, Vacuum birefringence as a probe of Planck scale noncommutativity, JHEP 09 (2006) 074 [hep-ph/0607188] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  13. [13]
    M.E. Peskin and D.V. Schroeder, An Introduction To Quantum Field Theory, Addison-Wesley, Reading U.S.A. (1995) [SPIRES].Google Scholar
  14. [14]
    M. Hayakawa, Perturbative analysis on infrared aspects of noncommutative QED on R 4, Phys. Lett. B 478 (2000) 394 [hep-th/9912094] [SPIRES].MathSciNetADSGoogle Scholar
  15. [15]
    M. Hayakawa, Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R 4, hep-th/9912167 [SPIRES].
  16. [16]
    M. Hayakawa, Perturbative ultraviolet and infrared dynamics of noncommutative quantum field theory, hep-th/0009098 [SPIRES].
  17. [17]
    G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [SPIRES].
  18. [18]
    D.A. Lowe, J. Polchinski, L. Susskind, L. Thorlacius and J. Uglum, Black hole complementarity versus locality, Phys. Rev. D 52 (1995) 6997 [hep-th/9506138] [SPIRES].MathSciNetADSGoogle Scholar
  19. [19]
    A.G. Cohen, D.B. Kaplan and A.E. Nelson, Effective field theory, black holes and the cosmological constant, Phys. Rev. Lett. 82 (1999) 4971 [hep-th/9803132] [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  20. [20]
    R. Banerjee, B.R. Majhi and S. Samanta, Noncommutative Black Hole Thermodynamics, Phys. Rev. D 77 (2008) 124035 [arXiv:0801.3583] [SPIRES].MathSciNetADSGoogle Scholar
  21. [21]
    P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Phys. Lett. B 632 (2006) 547 [gr-qc/0510112] [SPIRES].MathSciNetADSGoogle Scholar
  22. [22]
    Muon G-2 collaboration, G.W. Bennett et al., Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [SPIRES].ADSGoogle Scholar
  23. [23]
    R. Horvat, D. Kekez and J. Trampetic, Spacetime noncommutativity and ultra-high energy cosmic ray experiments, arXiv:1005.3209 [SPIRES].
  24. [24]
    G. Amelino-Camelia, G. Mandanici and K. Yoshida, On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes, JHEP 01 (2004) 037 [hep-th/0209254] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    S. Nobbenhuis, The cosmological constant problem, an inspiration for new physics, gr-qc/0609011 [SPIRES].
  26. [26]
    V.A. Kostelecky and M. Mewes, Sensitive polarimetric search for relativity violations in gamma-ray bursts, Phys. Rev. Lett. 97 (2006) 140401 [hep-ph/0607084] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    W. Behr et al., The Z → γγ/gg decays in the noncommutative standard model, Eur. Phys. J. C 29 (2003) 441 [hep-ph/0202121] [SPIRES].ADSGoogle Scholar
  28. [28]
    B. Melic, K. Passek-Kumericki and J. Trampetic, Quarkonia decays into two photons induced by the space-time non-commutativity, Phys. Rev. D 72 (2005) 054004 [hep-ph/0503133] [SPIRES].ADSGoogle Scholar
  29. [29]
    B. Melic, K. Passek-Kumericki and J. Trampetic, Kpi gamma decay and space-time noncommutativity, Phys. Rev. D 72 (2005) 057502 [hep-ph/0507231] [SPIRES].ADSGoogle Scholar
  30. [30]
    C. Tamarit and J. Trampetic, Noncommutative fermions and quarkonia decays, Phys. Rev. D 79 (2009) 025020 [arXiv:0812.1731] [SPIRES].ADSGoogle Scholar
  31. [31]
    M. Burić, D. Latas, V. Radovanović and J. Trampetic, Improved Zγγ decay in the renormalizable gauge sector of the noncommutative standard model, hep-ph/0611299 [SPIRES].
  32. [32]
    J. Trampetic, Renormalizability and Phenomenology of theta-expanded Noncommutative Gauge Field Theory, Fortschr. Phys. 56 (2008) 521 [arXiv:0802.2030] [SPIRES].MATHCrossRefMathSciNetGoogle Scholar
  33. [33]
    A. Alboteanu, T. Ohl and R. Ruckl, Probing the noncommutative standard model at hadron colliders, Phys. Rev. D 74 (2006) 096004 [hep-ph/0608155] [SPIRES].ADSGoogle Scholar
  34. [34]
    A. Alboteanu, T. Ohl and R. Ruckl, The Noncommutative Standard Model at O(θ 2), Phys. Rev. D 76 (2007) 105018 [arXiv:0707.3595] [SPIRES].ADSGoogle Scholar
  35. [35]
    S.M. Carroll, J.A. Harvey, V.A. Kostelecky, C.D. Lane and T. Okamoto, Noncommutative field theory and Lorentz violation, Phys. Rev. Lett. 87 (2001) 141601 [hep-th/0105082] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  36. [36]
    P. Schupp, J. Trampetic, J. Wess and G. Raffelt, The photon neutrino interaction in non-commutative gauge field theory and astrophysical bounds, Eur. Phys. J. C 36 (2004) 405 [hep-ph/0212292] [SPIRES].CrossRefADSGoogle Scholar
  37. [37]
    P. Minkowski, P. Schupp and J. Trampetic, Neutrino dipole moments and charge radii in non-commutative space-time, Eur. Phys. J. C 37 (2004) 123 [hep-th/0302175] [SPIRES].CrossRefADSGoogle Scholar
  38. [38]
    M. Haghighat, Bounds on the Parameter of Noncommutativity from Supernova SN1987A, Phys. Rev. D 79 (2009) 025011 [arXiv:0901.1069] [SPIRES].ADSGoogle Scholar
  39. [39]
    E. Akofor, A.P. Balachandran, A. Joseph, L. Pekowsky and B.A. Qureshi, Constraints from CMB on Spacetime Noncommutativity and Causality Violation, Phys. Rev. D 79 (2009) 063004 [arXiv:0806.2458] [SPIRES].ADSGoogle Scholar
  40. [40]
    R. Horvat and J. Trampetic, Constraining spacetime noncommutativity with primordial nucleosynthesis, Phys. Rev. D 79 (2009) 087701 [arXiv:0901.4253] [SPIRES].ADSGoogle Scholar
  41. [41]
    M. Chaichian, M.M. Sheikh-Jabbari and A. Tureanu, Hydrogen atom spectrum and the Lamb shift in noncommutative QED, Phys. Rev. Lett. 86 (2001) 2716 [hep-th/0010175] [SPIRES].CrossRefADSGoogle Scholar
  42. [42]
    A. Stern, Noncommutative Point Sources, Phys. Rev. Lett. 100 (2008) 061601 [arXiv:0709.3831] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  43. [43]
    M. Haghighat, S.M. Zebarjad and F. Loran, Positronium hyperfine splitting in non-commutative space at the order α 6, Phys. Rev. D 66 (2002) 016005 [hep-ph/0109105] [SPIRES].ADSGoogle Scholar
  44. [44]
    M. Haghighat and F. Loran, Three body bound state in noncommutative space, Phys. Rev. D 67 (2003) 096003 [SPIRES].ADSGoogle Scholar
  45. [45]
    V.V. Khoze and G. Travaglini, Wilsonian effective actions and the IR/UV mixing in noncommutative gauge theories, JHEP 01 (2001) 026 [hep-th/0011218] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  46. [46]
    T.J. Hollowood, V.V. Khoze and G. Travaglini, Exact results in noncommutative N = 2 supersymmetric gauge theories, JHEP 05 (2001) 051 [hep-th/0102045] [SPIRES].CrossRefMathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Physics DivisionRudjer Bošković InstituteZagrebCroatia

Personalised recommendations