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Super-Yang-Mills theory in SIM(1) superspace

Jiří Vohánka1 and Mir Faizal2

  • 1Department of Theoretical Physics and Astrophysics, Masaryk University, Kotlářská 267/2, 611 37 Brno, Czech Republic
  • 2Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

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Phys. Rev. D 91, 045015 – Published 13 February, 2015

DOI: https://doi.org/10.1103/PhysRevD.91.045015

Abstract

In this paper, we will analyze three-dimensional supersymmetric Yang-Mills theory coupled to matter fields in SIM(1) superspace formalism. The original theory which is invariant under the full Lorentz group has N=1 supersymmetry. However, when we break the Lorentz symmetry down to SIM(1) group, the SIM(1) superspace will break half the supersymmetry of the original theory. Thus, the resultant theory in SIM(1) superspace will have N=1/2 supersymmetry. This is the first time that N=1 supersymmetry will be broken down to N=1/2 supersymmetry, for a three-dimensional theory, on a manifold without a boundary. This is because it is not possible to use nonanticommutativity to break N=1 supersymmetry down to N=1/2 supersymmetry in three dimensions.

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References (46)

  1. V. A. Kostelecky and S. Samuel, Spontaneous breaking of Lorentz symmetry in string theory, Phys. Rev. D 39, 683 (1989).
  2. V. A. Kostelecky and S. Samuel, Gravitational phenomenology in higher dimensional theories and strings, Phys. Rev. D 40, 1886 (1989).
  3. N. Seiberg and E. Witten, String theory and noncommutative geometry, J. High Energy Phys. 09 (1999) 032.
  4. A. F. Ferrari, H. O. Girotti, and M. Gomes, Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections, Phys. Rev. D 73, 047703 (2006).
  5. J. Collins, A. Perez, D. Sudarsky, L. Urrutia, and H. Vucetich, Lorentz Invariance and Quantum Gravity: An Additional Fine-Tuning Problem?, Phys. Rev. Lett. 93, 191301 (2004).
  6. K. S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16, 953 (1977).
  7. S. W. Hawking and T. Hertog, Living with ghosts, Phys. Rev. D 65, 103515 (2002).
  8. P. Horava, Membranes at quantum criticality, J. High Energy Phys. 03 (2009) 020.
  9. P. Horava, Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point, Phys. Rev. Lett. 102, 161301 (2009).
  10. R. Gambini and J. Pullin, Nonstandard optics from quantum space-time, Phys. Rev. D 59, 124021 (1999).
  11. J. Alfaro, H. A. Morales-Tecotl, and L. F. Urrutia, Quantum Gravity Corrections to Neutrino Propagation, Phys. Rev. Lett. 84, 2318 (2000).
  12. A. G. Cohen and S. L. Glashow, Very Special Relativity, Phys. Rev. Lett. 97, 021601 (2006).
  13. M. M. Sheikh-Jabbari and A. Tureanu, Realization of Cohen-Glashow Very Special Relativity on Noncommutative Space-Time, Phys. Rev. Lett. 101, 261601 (2008).
  14. S. Cheon, C. Lee, and S. J. Lee, SIM(2)-invariant modifications of electrodynamic theory, Phys. Lett. B 679, 73 (2009).
  15. J. Alfaro and V. O. Rivelles, Non Abelian fields in very special relativity, Phys. Rev. D 88, 085023 (2013).
  16. A. G. Cohen and D. Z. Freedman, SIM(2) and SUSY, J. High Energy Phys. 07 (2007) 039.
  17. U. Lindstrom and M. Rocek, SIM(2) and superspace, arXiv:hep-th/0606093.
  18. S. Petras, R. von Unge, and J. Vohanka, SIM(2) and supergraphs, J. High Energy Phys. 07 (2011) 015.
  19. J. Vohanka, Gauge theory and SIM(2) superspace, Phys. Rev. D 85, 105009 (2012).
  20. N. Seiberg, Noncommutative superspace, N=1/2 supersymmetry, field theory and string theory, J. High Energy Phys. 06 (2003) 010.
  21. O. F. Dayi and L. T. Kelleyane, N=1/2 supersymmetric gauge theory in noncommutative space, Europhys. Lett. 78, 21004 (2007).
  22. T. Hatanaka and S. V. Ketov, N=1/2 supergravity with matter in four Euclidean dimensions, Nucl. Phys. B794, 495 (2008).
  23. S. V. Ketov and O. Lechtenfeld, Non-anticommutative solitons, Phys. Lett. B 663, 353 (2008).
  24. I. Jack, D. R. T. Jones, and R. Purdy, The non-anticommutative supersymmetric U(1) gauge theory, J. High Energy Phys. 04 (2009) 028.
  25. O. Lunin and S. J. Rey, Renormalizability of non(anti)commutative gauge theories with N=1/2 supersymmetry, J. High Energy Phys. 09 (2003) 045.
  26. A. F. Ferrari, M. Gomes, J. R. Nascimento, A. Y. Petrov, and A. J. da Silva, The three-dimensional non-anticommutative superspace, Phys. Rev. D 74, 125016 (2006).
  27. M. Faizal, Deformed Super-Yang-Mills in Batalin-Vilkovisky formalism, Int. J. Theor. Phys. 52, 392 (2013).
  28. D. V. Belyaev and P. van Nieuwenhuizen, Rigid supersymmetry with boundaries, J. High Energy Phys. 04 (2008) 008.
  29. M. Faizal and D. J. Smith, Supersymmetric Chern-Simons theory in presence of a boundary, Phys. Rev. D 85, 105007 (2012).
  30. D. S. Berman and D. C. Thompson, Membranes with a boundary, Nucl. Phys. B820, 503 (2009).
  31. M. Faizal and D. J. Smith, Non-anticommutativity in presence of a boundary, Phys. Rev. D 87, 025019 (2013).
  32. A. Gustavsson, Selfdual strings and loop space Nahm equations, J. High Energy Phys. 04 (2008) 083.
  33. J. Bagger and N. Lambert, Comments on multiple M2-branes, J. High Energy Phys. 02 (2008) 105.
  34. J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77, 065008 (2008).
  35. M. A. Bandres, A. E. Lipstein, and J. H. Schwarz, Studies of the ABJM theory in a formulation with manifest SU(4) R-symmetry, J. High Energy Phys. 09 (2008) 027.
  36. E. Antonyan and A. A. Tseytlin, On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory, Phys. Rev. D 79, 046002 (2009).
  37. O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, J. High Energy Phys. 10 (2008) 091.
  38. M. Schnabl and Y. Tachikawa, Classification of N=6 superconformal theories of ABJM type, J. High Energy Phys. 09 (2010) 103.
  39. O. K. Kwon, P. Oh, and J. Sohn, Notes on supersymmetry enhancement of ABJM theory, J. High Energy Phys. 08 (2009) 093.
  40. H. Samtleben and R. Wimmer, N=6 superspace constraints, SUSY enhancement and monopole operators, J. High Energy Phys. 10 (2010) 080.
  41. D. Bashkirov and A. Kapustin, Supersymmetry enhancement by monopole operators, J. High Energy Phys. 05 (2011) 015.
  42. A. Gustavsson, Monopoles, three-algebras and ABJM theories with N=5, 6, 8 supersymmetry, J. High Energy Phys. 01 (2011) 037.
  43. S. Mukhi and C. Papageorgakis, M2 to D2, J. High Energy Phys. 05 (2008) 085.
  44. Y. Pang and T. Wang, From N M2’s to N D2’s, Phys. Rev. D 78, 125007 (2008).
  45. P. M. Ho, Y. Imamura, and Y. Matsuo, M2 to D2 revisited, J. High Energy Phys. 07 (2008) 003.
  46. J. Kluson, D2 to M2 procedure for D2-brane DBI effective action, Nucl. Phys. B808, 260 (2009).

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Phys. Rev. D 91, 045015– Published 13 February, 2015
  • Received 24 September 2014

© 2015 American Physical Society

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