Can Seiberg-Witten Map Bypass Noncommutative Gauge Theory No-Go Theorem?
Abstract
There are strong restrictions on the possible representations and in general on the matter content of gauge theories formulated on noncommutative Moyal spaces, termed as noncommutative gauge theory no-go theorem. According to the no-go theorem \cite{no-go}, matter fields in the noncommutative U(1) gauge theory can only have or zero charges and for a generic noncommutative gauge theory matter fields can be charged under at most two of the gauge group factors. On the other hand, it has been argued in the literature that, since a noncommutative U(N) gauge theory can be mapped to an ordinary U(N) gauge theory via the Seiberg-Witten map, seemingly it can bypass the no-go theorem. In this note we show that the Seiberg-Witten map \cite{SW} can only be consistently defined and used for the gauge theories which respect the no-go theorem. We discuss the implications of these arguments for the particle physics model building on noncommutative space.
Cite
@article{arxiv.0907.2646,
title = {Can Seiberg-Witten Map Bypass Noncommutative Gauge Theory No-Go Theorem?},
author = {M. Chaichian and P. Presnajder and M. M. Sheikh-Jabbari and A. Tureanu},
journal= {arXiv preprint arXiv:0907.2646},
year = {2010}
}
Comments
16 pages; typos and formulas (2.29) and (2.30) corrected