Self-energies on deformed spacetimes

Abstract

We study one-loop photon (Pi) and neutrino (Sigma) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor theta^{mu nu}. For the general fermion-photon (S_f) and photon self-interaction (S_g) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(mu^2(theta p)^2). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon self-energy in four-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of theta^{mu nu} and setting deformation parameters (kappa_f,kappa_g)=(0,3). In this case the neutrino two-point function vanishes. Thus for a specific point (0,3) in the parameter-space (kappa_f,kappa_g), a covariant theta-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (kappa_f,kappa_g) combinations, the neutrino self-energy still contains an superficial IR divergence.

D-dimensional photon-loop contribution added to the photon self-energy; version to appear in JHEP, 29 pages, 3 figures, 1 table

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Cited by in corpus (17)

• Noncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map
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• Quantum duality under the theta-exact Seiberg-Witten map
• Photon self-interaction on deformed spacetime
• Seiberg-Witten map Invariant Scatterings
• SO(10) GUTs with large tensor representations on Noncommutative Space-time
• Spacetime Deformation Effect on the Early Universe and the PTOLEMY Experiment
• Two-Point Functions on Deformed Spacetime
• The theta-exact Seiberg-Witten maps at the e3 order
• The hybrid Seiberg-Witten map, its $\theta$-exact expansion and the antifield formalism
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences
• Inferring type and scale of noncommutativity from the PTOLEMY experiment
• Search for associated production of Higgs with Z boson in the noncommutative Standard Model at linear colliders
• Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution
• Revisiting NCQED and scattering amplitudes
• UV/IR mixing in Noncommutative SU(N) Yang-Mills theory