Skip to main content
SpringerLink
Log in

Non-Abelian Gauge Theory in the Lorentz Violating Background

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ’t Hooft, G.: Quantization of point particles in (2 + 1)-dimensional gravity and space-time discreteness, Class. Quant. Grav. 13, 1023 (1996)

    Article  ADS  MATH  Google Scholar 

  2. Amelino-Camelia, G., Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., Sarkar, S.: Tests of quantum gravity from observations of gamma-ray bursts. Nature 393, 763 (1998)

    Article  ADS  Google Scholar 

  3. Gambini, R., Pullin, J.: Nonstandard optics from quantum space-time. Phys. Rev. D 59, 124021 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  4. Carroll, S.M., Harvey, J.A., Kostelecky, V.A., Lane, C. D., Okamoto, T.: Noncommutative field theory and Lorentz violation. Phys. Rev. Lett. 87, 141601 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  5. Horava, P.: Quantum gravity at a lifshitz point. Phys. Rev. D 79, 084008 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. Chakravarty, S., Dasgupta, K., Ganor, O.J., Rajesh, G.: Pinned branes and new nonLorentz invariant theories. Nucl. Phys. B 587, 228 (2000)

    Article  ADS  MATH  Google Scholar 

  7. Kostelecky, V.A., Samuel, S.: Gravitational phenomenology in higher dimensional theories and strings. Phys. Rev. D 40, 1886 (1989)

    Article  ADS  Google Scholar 

  8. Cohen, A.G., Glashow, S.L.: Very special relativity. Phys. Rev. Lett. 97, 021601 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Sheikh-Jabbari, M.M., Tureanu, A.: Realization of Cohen-Glashow very special relativity on noncommutative space-time. Phys. Rev. Lett. 101, 261601 (2008)

    Article  ADS  Google Scholar 

  10. Cohen, A.G., Freedman, D.Z.: SIM(2) and SUSY. JHEP 0707, 039 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  11. Petras, S., von Unge, R., Vohanka, J.: SIM(2) and supergraphs. JHEP 1107, 015 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Vohanka, J.: Gauge theory and SIM(2) superspace. Phys. Rev. D 85, 105009 (2012)

    Article  ADS  Google Scholar 

  13. Vohánka, J., Faizal, M.: Chern–simons theory in SIM(1) superspace. Eur. Phys. J. C 75(12), 592 (2015)

    Article  ADS  Google Scholar 

  14. Vohánka, J., Faizal, M.: Supersymmetric Chern–Simons theory in presence of a boundary in the light-like direction. Nucl. Phys. B 904, 327 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Vohánka, J., Faizal, M.: Super-Yang-Mills theory in SIM(1) superspace. Phys. Rev. D 91(4), 045015 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  16. Kouretsis, A.P., Stathakopoulos, M., Stavrinos, P.C.: The general very special relativity in finsler cosmology. Phys. Rev. D 79, 104011 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. Muck, W.: Very special relativity in curved Space-Times. Phys. Lett. B 670, 95 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  18. Shah, M.B., Ganai, P.A.: A study of gaugeon formalism for QED in lorentz violating background. Commun. Theor. Phys. 69(2), 166 (2018)

    Article  ADS  Google Scholar 

  19. Masood, S., Shah, M.B., Ganai, P.A.: Spontaneous symmetry breaking in Lorentz violating background. Int. J. Geom. Meth. Mod. Phys. 15(02), 1850021 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  20. Shah, M.B., Ganai, P.A.: Quantum gauge freedom in the Lorentz violating background. Int. J. Geom. Meth. Mod. Phys. 15(01), 1850009 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. Bufalo, R., Upadhyay, S.: Axion mass bound in very special relativity. Phys. Lett. B 772, 420 (2017)

    Article  ADS  MATH  Google Scholar 

  22. Upadhyay, S.: Reducible gauge theories in very special relativity. Eur. Phys. J. C 75(12), 593 (2015)

    Article  ADS  Google Scholar 

  23. Ahluwalia, D.V., Horvath, S.P.: Very special relativity as relativity of dark matter: The Elko connection. JHEP 1011, 078 (2010)

    Article  ADS  MATH  Google Scholar 

  24. Chang, Z., Li, M.H., Li, X., Wang, S.: Cosmological model with local symmetry of very special relativity and constraints on it from supernovae. Eur. Phys. J. C 73(6), 2459 (2013)

    Article  ADS  Google Scholar 

  25. Alfaro, J., Rivelles, V.O.: Non Abelian fields in very special relativity. Phys. Rev. D 88, 085023 (2013)

    Article  ADS  Google Scholar 

  26. Alfaro, J., González, P., Ávila, R.: Electroweak standard model with very special relativity. Phys. Rev. D 91, 105007 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  27. Alfaro, J., González, P., Ávila, R.: Addendum: Phys. Rev. D 91(12), 129904 (2015)

    ADS  Google Scholar 

  28. Becchi, C., Rouet, A., Stora, R.: Renormalization of gauge theories. Annals Phys. 98, 287 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  29. Tyutin, I.V.: Gauge invariance in field theory and statistical physics in operator formalism

  30. Costa, G., Julve, J., Marinucci, T., Tonin, M.: Nonabelian gauge theories and triangle anomalies. Nuovo Cim. A 38, 373 (1977)

    Article  ADS  Google Scholar 

  31. Kugo, T., Ojima, I.: Manifestly covariant canonical formulation of Yang-Mills field theories: Physical state subsidiary conditions and physical s matrix unitarity. Phys. Lett. 73B, 459 (1978)

    Article  ADS  Google Scholar 

  32. Hata, H., Kugo, T.: Subsidiary conditions and physical s matrix unitarity in covariant canonical formulation of supergravity. Nucl. Phys. B 158, 357 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  33. Faizal, M., Khan, M.: A superspace formulation of the BV action for higher derivative theories. Eur. Phys. J. C 71, 1603 (2011)

    Article  ADS  Google Scholar 

  34. Baulieu, L., Thierry-Mieg, J.: The principle of BRS symmetry: an alternative approach to Yang-Mills theories. Nucl. Phys. B 197, 477 (1982)

    Article  ADS  Google Scholar 

  35. Azevedo, T., Jusinskas, R.L.: Background constraints in the infinite tension limit of the heterotic string. JHEP 1608, 133 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  36. Mafra, C.R., Schlotterer, O.: One-loop superstring six-point amplitudes and anomalies in pure spinor superspace. JHEP 1604, 148 (2016)

    ADS  Google Scholar 

  37. Jusinskas, R.L.: On the field-antifield (a)symmetry of the pure spinor superstring. JHEP 1512, 136 (2015)

    ADS  MathSciNet  Google Scholar 

  38. Jusinskas, R.L.: Notes on the ambitwistor pure spinor string. JHEP 1605, 116 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  39. Oda, I.: Covariant matrix model of superparticle in the pure spinor formalism. Mod. Phys. Lett. A 18, 1023 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Faizal, M.: Aspects of ABJ theory. JHEP 1301, 156 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Faizal, M.: Chern-Simons-Matter theory. Int. J. Mod. Phys. A 28, 1350012 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Faizal, M., Upadhyay, S., Mandal, B.P.: IR Finite graviton propagators in de Sitter spacetime. Eur. Phys. J. C 76(4), 189 (2016)

    Article  ADS  Google Scholar 

  43. Chang, L.N., Soo, C.p.: BRST cohomology and invariants of 4-D gravity in Ashtekar variables. Phys. Rev. D 46, 4257 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  44. Kachru, S.: Extra states symmetries in D < 2 closed string theory. Nucl. Phys. B 390, 173 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  45. Terao, H.: Quantum analysis of Jackiw and Teitelboim’s model for (1 + 1)-D gravity and topological gauge theory. Nucl. Phys. B 395, 623 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  46. Lee, H.Y., Nakamichi, A., Ueno, T.: Topological two form gravity in four-dimensions. Phys. Rev. D 47, 1563 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  47. Ohta, N., Suzuki, H.: Interactions of discrete states with nonzero ghost number in c = 1 2-D gravity. Mod. Phys. Lett. A 7, 2723 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Anselmi, D., Fre, P.: Twisted N = 2 supergravity as topological gravity in four-dimensions. Nucl. Phys. B 392, 401 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  49. Faizal, M.: Noncommutativity and non-anticommutativity in perturbative quantum gravity. Mod. Phys. Lett. A 27, 1250075 (2012)

    Article  ADS  MATH  Google Scholar 

  50. Faizal, M.: Noncommutative quantum gravity. Mod. Phys. Lett. A 28, 1350034 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  51. Faizal, M.: Noether‘s charge in the super-group field cosmology. Grav. Cosmol. 20(2), 132 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Faizal, M.: Absence of black holes information paradox in group field cosmology. Int. J. Geom. Meth. Mod. Phys. 11, 1450010 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  53. Faizal, M.: Super-group field cosmology. Class. Quant. Grav. 29, 215009 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. Troost, J.: Massless particles on supergroups and A d S 3 x S 3 supergravity. JHEP 1107, 042 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. Faizal, M.: The BV formalization of Chern-Simons theory on deformed superspace. Commun. Theor. Phys. 58, 704 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  56. Banerjee, R., Deguchi, S.: A superspace formulation of Yang-Mills theory on sphere. J. Math. Phys. 51, 052301 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. Ulker, K.: N = 2 SYM action as a BRST exact term, topological Yang-Mills and instantons. Phys. Rev. D 68, 085005 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  58. Shah, M.B., Faizal, M., Ganai, P.A., Zaz, Z., Bhat, A., Masood, S.: Boundary effects in Super-Yang–Mills theory. Eur. Phys. J. C 77(5), 309 (2017)

    Article  ADS  Google Scholar 

  59. Lehum, A.C., Nascimento, J.R., Petrov A.Y., da Silva, A. J.: Supergauge theories in aether superspace. Phys. Rev. D 88, 045022 (2013)

    Article  ADS  Google Scholar 

  60. Weinreb, P., Faizal, M.: Generalized Faddeev–Popov method for a deformed supersymmetric Yang–Mills theory. Phys. Lett. B 748, 102 (2015)

    Article  ADS  MATH  Google Scholar 

  61. Upadhyay, S., Panigrahi, P.K.: Quantum gauge freedom in very special relativity. Nucl. Phys. B 915, 168 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. Upadhyay, S., Shah, M.B., Ganai, P.A.: Lorentz violating p-form gauge theories in superspace. Eur. Phys. J. C 77(3), 157 (2017)

    Article  ADS  Google Scholar 

  63. Capri, M.A.L., Sobreiro, R.F., Sorella, S. P.: Interpolating among the Landau, Coulomb and maximal Abelian gauges. Phys. Rev. D 73, 041701 (2006)

    Article  ADS  MATH  Google Scholar 

  64. Dudal, D., Gracey, J.A., Lemes, V.E.R., Sarandy, M.S., Sobreiro, R.F., Sorella, S.P., Verschelde, H.: An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge. Phys. Rev. D 70, 114038 (2004)

    Article  ADS  MATH  Google Scholar 

  65. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1113 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  66. Maldacena, J.M.: Adv. Theor. Math. Phys. 2, 231 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  67. Gustavsson, A.: Selfdual strings and loop space Nahm equations. JHEP 0804, 083 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  68. Bagger, J., Lambert, N.: Comments on multiple M2-branes. JHEP 0802, 105 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  69. Bagger, J., Lambert, N.: Gauge symmetry and supersymmetry of multiple M2-branes. Phys. Rev. D 77, 065008 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  70. Faizal, M.: Deformation of the ABJM theory. Europhys. Lett. 98, 31003 (2012)

    Article  ADS  Google Scholar 

  71. Aharony, O., Bergman, O., Jafferis, D.L., Maldacena, J.: N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals. JHEP 0810, 091 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  72. Aharony, O., Bergman, O., Jafferis, D.L.: Fractional M2-branes. JHEP 0811, 043 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  73. Faizal, M.: Non-anticommutative ABJ theory. Nucl. Phys. B 869, 598 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  74. Queiruga, J.M., Lehum, A.C., Faizal, M.: Kählerian effective potentials for Chern–Simons-matter theories. Nucl. Phys. B 902, 58 (2016)

    Article  ADS  MATH  Google Scholar 

  75. Antonyan, E., Tseytlin, A.A.: On 3d N = 8 Lorentzian BLG theory as a scaling limit of 3d superconformal N = 6 ABJM theory. Phys. Rev. D 79, 046002 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  76. Berman, D.S., Perry, M.J., Sezgin, E., Thompson, D.C.: Boundary conditions for interacting membranes. JHEP 1004, 025 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  77. Aprile, F., Niarchos, V.: \(\mathcal {N} = 2\) supersymmetric field theories on 3-manifolds with A-type boundaries. JHEP 1607, 126 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  78. Faizal, M.: Gauge and supersymmetric invariance of a boundary Bagger-Lambert-Gustavsson theory. JHEP 1204, 017 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  79. Belyaev, D.V., van Nieuwenhuizen, P.: Simple d = 4 supergravity with a boundary. JHEP 0809, 069 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  80. Faizal, M., Luo, Y., Smith, D.J., Tan, M.C., Zhao, Q.: Gauge and supersymmetry invariance of N = 2 boundary Chern–Simons theory. Nucl. Phys. B 914, 577 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  81. Faizal, M.: Boundary effects in the BLG theory. Mod. Phys. Lett. A 29(31), 1450154 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  82. Berman, D.S., Thompson, D.C.: Membranes with a boundary. Nucl. Phys. B 820, 503 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  83. Faizal, M., Smith, D.J.: Nonanticommutativity in the presence of a boundary. Phys. Rev. D 87(2), 025019 (2013)

    Article  ADS  Google Scholar 

  84. Bilal, A.: Supersymmetric boundaries and junctions in four dimensions. JHEP 1111, 046 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  85. Belyaev, D.V., Pugh, T.G.: The Supermultiplet of boundary conditions in supergravity. JHEP 1010, 031 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  86. Faizal, M., Awad, A.: Four dimensional supersymmetric theories in presence of a boundary. Phys. Lett. B 748, 414 (2015)

    Article  ADS  MATH  Google Scholar 

  87. Belyaev, D.V., van Nieuwenhuizen, P.: Rigid supersymmetry with boundaries. JHEP 0804, 008 (2008)

    Article  ADS  Google Scholar 

  88. Gribov, V.N.: Quantization of nonabelian gauge theories. Nucl. Phys. B 139, 1 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  89. Singer, I.M.: Some remarks on the gribov ambiguity. Commun. Math. Phys. 60, 7 (1978)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  90. Shigemoto, K.: Field strength method and Gribov ambiguity in two-dimensional Nonabelian gauge theory. Lett. Nuovo Cim. 24, 495 (1979)

    Article  Google Scholar 

  91. Killingback, T.P.: The gribov ambiguity in gauge theories on the 4 torus. Phys. Lett. 138B, 87 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  92. Zwanziger, D.: Nonperturbative modification of the Faddeev-popov formula and banishment of the naive vacuum. Nucl. Phys. B 209, 336 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  93. Zwanziger, D.: Local and renormalizable action from the gribov horizon. Nucl. Phys. B 323, 513 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  94. Capri, M. A. L., Dudal, D., Pereira, A. D., Fiorentini, D., Guimaraes, M.S., Mintz, B.W., Palhares, L.F., Sorella, S.P.: Nonperturbative aspects of Euclidean Yang-Mills theories in linear covariant gauges: Nielsen identities and a BRST-invariant two-point correlation function. Phys. Rev. D 95(4), 045011 (2017)

    Article  ADS  Google Scholar 

  95. Zwanziger, D.: Action from the gribov horizon. Nucl. Phys. B 321, 591 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  96. Guimaraes, M.S., Pereira, A.D., Sorella, S.P.: Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory. Phys. Rev. D 94(11), 116011 (2016)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, National Institute of Technology, Srinagar, Kashmir, 190006, India

    Prince A. Ganai & Mushtaq B. Shah

  2. Department of Physics, International Islamic University, H-10 Sector, Islamabad, 44000, Pakistan

    Masood Syed

  3. Department of Mathematics, National Institute of Technology, Srinagar, Kashmir, 190006, India

    Owais Ahmad

Authors
  1. Prince A. Ganai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mushtaq B. Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masood Syed
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Owais Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mushtaq B. Shah.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ganai, P.A., Shah, M.B., Syed, M. et al. Non-Abelian Gauge Theory in the Lorentz Violating Background. Int J Theor Phys 57, 1974–1982 (2018). https://doi.org/10.1007/s10773-018-3722-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3722-6

Keywords

Search

Navigation