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Paper   IPM / Physic / 11151
School of Physics
  Title:   Can Seiberg-Witten Map Bypass the Noncommutative Gauge Theory No-Go Theorem?
1.  M. Chaichian
2.  P. Presnajder
3.  M.M. Sheikh-Jabbari
4.  A. Tureanu
  Status:   Published
  Journal: Phys. Lett. B
  Vol.:  683
  Year:  2009
  Pages:   55-61
  Supported by:  IPM
There are strong restrictions on the possible representations and in general matter content of gauge theories formulated on noncommutative Moyal spaces, termed as noncommutative gauge theory no-go theorem [arXiv:hep-th/0107037]. According to the no-go theorem matter fields in the noncommutative U(1) gauge theory can only have ±1 or zero charges and for a generic noncommutative ∏i=1n U(Ni) gauge theory matter fields can at most be charged under two of the U(Ni) gauge group factors. On the other hand it has been argued that a noncommutative U(N) gauge theory can be mapped to a commutative U(N) gauge theory, via the Seiberg-Witten map [arXiv:hep-th/9908142] and hence seemingly bypass the no-go theorem. In this note we show that the Seiberg-Witten map can only be consistently defined and used for the gauge theories which respect the no-go theorem stated in [arXiv:hep-th/0107037]. We discuss the implications of these arguments for the particle physics model building on noncommutative space.

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