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|Paper IPM / Physic / 11151||
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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