Noncommutative GUT inspired theories with U(1), SU(N) groups and their renormalisability

Abstract

We consider the 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 theta, 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(theta) triple gauge-field interactions vanish, the divergences can be absorbed by means of multiplicative renormalisations and the inclusion of theta-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 non-chiral. 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 renormalisable matter sector, but are on-shell one-loop multiplicatively renormalisable at order one in theta.

33 pages, 7 figures. Version 2: Section 5 was simplified, Section 6 was expanded with more discussions, references were added

References in corpus (7)

• Improved Z -> gamma gamma decay in the renormalizable gauge sector of the noncommutative standard model
• Probing the Noncommutative Standard Model at Hadron Colliders
• Non-commutative SU(N) gauge theories and asymptotic freedom
• The absence of the 4$\psi$ divergence in noncommutative chiral models
• Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions
• Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Cited by in corpus (11)

• Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory
• Computing the θ-exact Seiberg-Witten map for arbitrary gauge groups
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• Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion
• Yukawa terms in noncommutative SO(10) and E6 GUTs
• SO(10) GUTs with large tensor representations on Noncommutative Space-time
• The Minimal and the New Minimal Supersymmetric Grand Unified Theories on Noncommutative Space-time
• Laboratory frame analysis of $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ scattering in the Noncommutative Standard Model
• The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics
• Twisted SUSY: twisted symmetry versus renormalizability
• NC GUTs: A Status Report