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} ~ θ^{-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.

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)

References in corpus (8)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Comments on Non-Commutative Phenomenology
• UV/IR Mixing via Closed Strings and Tachyonic Instabilities
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Exact Results in Noncommutative $\mathcal{N}=2$ Supersymmetric Gauge Theories
• *-Wars Episode I: The Phantom Anomaly
• Dynamical Breaking of Supersymmetry in Noncommutative Gauge Theories

Cited by in corpus (11)

• Non-Commutative GUTs, Standard Model and C,P,T
• Gauge Covariance of the Aharonov-Bohm Phase in Noncommutative Quantum Mechanics
• Can Seiberg-Witten Map Bypass Noncommutative Gauge Theory No-Go Theorem?
• Spontaneous reduction of noncommutative gauge symmetry and model building
• Circumventing the No-Go Theorem in Noncommutative Gauge Field Theory
• The static effective action for non-commutative QED at high temperature
• Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories
• A Noncommutative Version of the Minimal Supersymmetric Standard Model
• Classical transport equation in non-commutative QED at high temperature
• Transport equation for the photon Wigner operator in non-commutative QED
• Twisted invariances of noncommutative gauge theories