Research PapersNo Access

LORENTZ INVARIANT AND SUPERSYMMETRIC INTERPRETATION OF NONCOMMUTATIVE QUANTUM FIELD THEORY

Department of Physics, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan

Search for more papers by this author

and

SHIN SASAKI

Department of Physics, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan

Search for more papers by this author

https://doi.org/10.1142/S0217751X05022421Cited by:29 (Source: Crossref)

Abstract

In this paper, using a Hopf-algebraic method, we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincaré algebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired SUSY in non(anti)commutative superspace.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

H. S. Snyder, Phys. Rev. 71, 38 (1947), DOI: 10.1103/PhysRev.71.38. Crossref, Web of Science, ADS, Google Scholar
N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999). ADS, Google Scholar
R. J. Szabo, Phys. Rep. 378, 207 (2003), DOI: 10.1016/S0370-1573(03)00059-0. Crossref, Web of Science, ADS, Google Scholar
M. R. Douglas and N. A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001), DOI: 10.1103/RevModPhys.73.977. Crossref, Web of Science, ADS, Google Scholar
N. Seiberg, J. High Energy Phys. 0306, 010 (2003). ADS, Google Scholar
T. Araki, K. Ito and A. Ohtsuka, Phys. Lett. B 573, 209 (2003). Crossref, Web of Science, ADS, Google Scholar
T. Araki, K. Ito and A. Ohtsuka, J. High Energy Phys. 0401, 046 (2004); T. Araki and K. Ito, Phys. Lett. B 595, 513 (2004) . Google Scholar
S. Ferrara and M. A. Lledó, J. High Energy Phys. 0005, 008 (2000). Crossref, ADS, Google Scholar
D. Klemm, S. Penati and L. Tamassia, Class. Quantum Grav. 20, 2905 (2003), DOI: 10.1088/0264-9381/20/13/333. Crossref, Web of Science, Google Scholar
H. Ooguri and C. Vafa, Adv. Theor. Math. Phys. 7, 53 (2003); ibid. 7, 405 (2004) . Google Scholar
N. Berkovits and N. Seiberg, J. High Energy Phys. 0307, 010 (2003). ADS, Google Scholar
J. de Boer, P. A. Grass and P. van Nieuwenhuizen, Phys. Lett. B 574, 98 (2003). Crossref, Web of Science, ADS, Google Scholar
M. Chaichianet al., Phys. Lett. B 604, 98 (2004). Crossref, Web of Science, ADS, Google Scholar
M. Chaichian, P. Presnajder and A. Tureanu, New concept of relativistic invariance in NC space–time: Twisted Poincaré symmetry and its implications, hep-th/0409096 . Google Scholar
C. Chryssomalakos, Physics, combinatorics and Hopf algebras, hep-th/0408165 . Google Scholar
V. Chari and A. Pressley , A Guide to Quantum Groups ( Cambridge University Press , Cambridge , 1994 ) . Google Scholar
P. P. Kulish and A. I. Mudrov, Proc. Steklov. Math. Inst. 226, 97 (1999). Google Scholar
N. Reshetikhin, Lett. Math. Phys. 20, 331 (1990), DOI: 10.1007/BF00626530. Crossref, Web of Science, ADS, Google Scholar
J. Fuchs , Affine Lie Algebras and Quantum Groups ( Cambridge University Press , Cambridge , 1992 ) . Google Scholar
Y. Zhang and M. D. Gould, J. Math. Phys. 40, 5264 (1999), DOI: 10.1063/1.533029. Crossref, Web of Science, ADS, Google Scholar
S. Ferrara and E. Sokatchev, Phys. Lett. B 579, 226 (2004). Crossref, Web of Science, ADS, Google Scholar
S. V. Ketov and S. Sasaki, Phys. Lett. B 595, 530 (2004); ibid. 597, 105 (2004); SU(2) × U(1) nonanticommutative N = 2 supersymmetric gauge theory, hep-th/0407211 . Google Scholar
E. Ivanov, O. Lechtenfeld and B. Zupnik, J. High Energy Phys. 0402, 012 (2004). ADS, Google Scholar
S. Ferrara, E. Ivanov, O. Lechtenfeld, E. Sokatchev and B. Zupnik Non-anticommutative chiral singlet deformation of N = (1, 1) gauge theory, hep-th/0405049 . Google Scholar
M. F. Sohnius, Nucl. Phys. B 138, 109 (1978), DOI: 10.1016/0550-3213(78)90159-1. Crossref, Web of Science, ADS, Google Scholar
A. A. Zheltukhin and U. Lindstrom, J. High Energy Phys. 0201, 034 (2002); Nucl. Phys. Proc. Suppl. 102, 126 (2001); D. V. Uvarov and A. A. Zheltukhin, J. High Energy Phys. 0403, 063 (2004) . Google Scholar
S. Hewson, Nucl. Phys. B 507, 445 (1997). Web of Science, Google Scholar
S. Ferrara, M. A. Lledo and O. Macia, J. High Energy Phys. 0309, 068 (2003). ADS, Google Scholar
R. Oeckl, Nucl. Phys. B 571, 559 (2000). Crossref, Web of Science, Google Scholar
P. Kosinski, J. Lukierski and P. Maslanka, Quantum deformations of space–time SUSY and noncommutative superfield theory, hep-th/0011053 . Google Scholar