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Asymptotic behavior of Lorentz violation on orbifolds

Momentum dependence of quantum corrections with higher-dimensional Lorentz violation is examined in electrodynamics on orbifolds. It is shown that effects of the Lorentz violation are not decoupled at high energy scales. Despite the loss of the higher-dimensional Lorentz invariance, a higher-dimensional Ward identity is found to be fulfilled for one-loop vacuum polarization. This implies that gauge invariance may be prior to Lorentz invariance as a guiding principle in higher-dimensional field theory. As a universal application of electrodynamics, an extra-dimensional aspect for Furry's theorem is emphasized.