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As recently pointed out, regularization schemes defined in four-dimensionsmay also face inconsistencies in the presence of chiral fermions. In this work,we extend this analysis to two-loop order. Adopting the implicit regularizationas working arena, we discuss in detail how a consistent version of the methodcan be envisaged, and present many of the subtleties that appear at two-looporder using an abelian chiral model as working example.

A step towards a consistent treatment of chiral theories at higher loop order: the abelian case