Noncommutativity and Model Building

Abstract

We propose a way to introduce matter fields transforming in arbitrary representations of the gauge group in noncommutative U(N) gauge theories. We then argue that in the presence of supersymmetry, an ordinary commutative SU(N) gauge theory with a general matter content can always be embedded into a noncommutative U(N) theory at energies above the noncommutativity mass scale M_{NC} ~ \theta^{-1/2}. At energies below M_{NC}, the U(1) degrees of freedom decouple due to the IR/UV mixing, and the noncommutative theory reduces to its commutative counterpart. Supersymmetry can be spontaneously broken by a Fayet-Iliopoulos D-term introduced in the noncommutative U(N) theory. U(1) degrees of freedom become arbitrarily weakly coupled in the infrared and naturally play the role of the hidden sector for supersymmetry breaking. To illustrate these ideas we construct a noncommutative U(5) GUT model with Fayet-Iliopoulos supersymmetry breaking, which reduces to a realistic commutative theory in the infrared.

Comments: 8 pages, v2: equation (26) corrected, a comment and references added; v3: add comments about anomaly cancellation; stressing main technical achievement is the construction of matters in arbitrary representations of noncommutative U(N)