Dynamical breaking of supersymmetry in noncommutative gauge theories

We propose a new mechanism of spontaneous supersymmetry breaking in noncommutative gauge theories. We find that in N=1 noncommutative gauge theories both supersymmetry and gauge invariance are dynamically broken. Supersymmetry is broken spontaneously by a Fayet–Iliopoulos D-term which naturally arises in a noncommutative U(n) theory. For a non-chiral matter content the Fayet–Iliopoulos term is not renormalized and its tree-level value can be chosen to be much smaller than the relevant string/noncommutativity scale. In the low energy theory, the noncommutative U(n) gauge symmetry is broken down to a commutative U(1)×SU(n). This breaking is triggered by the IR/UV mixing and manifests itself at and below the noncommutativity mass scale MNC∼θ−1/2. In particular, the U(1) degrees of freedom decouple from the SU(n) in the infrared and become arbitrarily weakly coupled, thus playing the role of the hidden sector for supersymmetry breaking.