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Paper IPM / Physic / 11151  


Abstract:  
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 nogo theorem [arXiv:hepth/0107037]. According to the nogo theorem matter fields in the noncommutative U(1) gauge theory can only have ±1 or zero charges and for a generic noncommutative ∏_{i=1}^{n} U(N_{i}) gauge theory matter fields can at most be charged under two of the U(N_{i}) 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 SeibergWitten map [arXiv:hepth/9908142] and hence seemingly bypass the nogo theorem. In this note we show that the SeibergWitten map can only be consistently defined and used for the gauge theories which respect the nogo theorem stated in [arXiv:hepth/0107037]. We discuss the implications of these arguments for the particle physics model building on noncommutative space.
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