2009/10/31 by Carlos Tamarit, C. Tamarit · 13 citations
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Fermion #Field (mathematics) #Gauge theory #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #hep-th
paper · pdf · doi:10.1103/physrevd.81.025006
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 81(2) (American Physical Society) · 33 pages, 7 figures. Version 2: Section 5 was simplified, Section 6 was expanded with more discussions, references were added
arxiv created 2010/01/11 · openalex publication_date 2010/01/11 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the grand unified theory (GUT)-compatible formulation of noncommutative QED, as well as noncommutative SU(N) GUTs, for N>2, with no scalars but with fermionic matter in an arbitrary, anomaly-free representation, in the enveloping-algebra approach. We compute, to first order in the noncommutativity parameters \ensuremathθ^\ensuremathμ\ensuremathν, the UV divergent part of the one-loop background-field effective action involving at most two fermion fields and an arbitrary number of gauge fields. It turns out that, for special choices of the ambiguous trace over the gauge degrees of freedom, for which the O(\ensuremathθ) triple gauge-field interactions vanish, the divergences can be absorbed by means of multiplicative renormalizations and the inclusion of \ensuremathθ-dependent counterterms that vanish on shell and are thus unphysical. For this to happen in the SU(N), N>2 case, the representations of the matter fields must have a common second Casimir; anomaly cancellation then requires the ordinary (commutative) matter content to be nonchiral. Together with the vanishing of the divergences of fermionic four point functions, this shows that GUT-inspired theories with U(1) and SU(N), N>2 gauge groups and ordinary vector matter content not only have a renormalizable matter sector, but are on-shell one-loop multiplicatively renormalizable at order one in \ensuremathθ.