Photon self-interaction on deformed spacetime

Abstract

A novel nonlocal four-photon interaction on the deformed spacetime is derived and studied in the three selected models (I, II, III). The first two models (I, II) are obtained via two distinct second-order $\theta$-exact Seiberg-Witten maps of the noncommutative U(1) gauge field strength on Moyal space. The third one (III), inspired by the manifestly gauge invariant structures emerging in the first two, due to the model generality has been constructed with a different set of freedom parameters. The physical relevancy of all models is analyzed by evaluating the four-photon-tadpole diagram, which, when combined with the bubble graph, enables us to fully consider all contributions to the one-loop photon polarization tensor. For an arbitrary noncommutative matrix theta^μν, the full quadratic IR divergence cancellation in the one-loop photon two-point function is obtained with particular combinations of Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II. Finally, our model III enables complete elimination of all pathological terms in the photon polarization tensor at one-loop order if a special value for the theta matrix is chosen.

24 pages, 3 figures. Version published in Physical Review D 92, 125006 (2015). arXiv admin note: text overlap with arXiv:1506.02864

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• Non-commutative SU(N) gauge theories and asymptotic freedom
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• Noncommutative SO(2,3) gauge theory and noncommutative gravity
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• Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences
• Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution
• Inferring type and scale of noncommutativity from the PTOLEMY experiment
• Revisiting NCQED and scattering amplitudes
• Bounds on the scale of noncommutativity from mono photon production in ATLAS Runs -1 and -2 experiments at LHC energies
• UV/IR mixing in Noncommutative SU(N) Yang-Mills theory