Noncommutative Gauge Field Theories: A No-Go Theorem

Details Noncommutative Gauge Field Theories: A No-Go Theorem Noncommutative Gauge Field Theories: A No-Go Theorem

2001-07-05

arxiv.org/abs/hep-th/0107037v1

Phys.Lett.B526:132-136,2002

Physics

High Energy Physics

High Energy Physics - Theory

latex, 4 pages

Scientific paper

10.1016/S0370-2693(01)01478-2

Studying the general structure of the noncommutative (NC) local groups, we prove a no-go theorem for NC gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local NC $u(n)$ {\it algebra} only admits the irreducible n by n matrix-representation. Hence the gauge fields are in n by n matrix form, while the matter fields {\it can only be} in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple-group factors, the matter fields can transform nontrivially under {\it at most two} NC group factors. In other words, the matter fields cannot carry more than two NC gauge group charges. This no-go theorem imposes strong restrictions on the NC version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED.

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