We investigate analytic properties of string-integrated massless correlation functions and propagators with emphasis on their infrared behaviour. These are relevant in various models of quantum field theory with massless fields, including QED.

Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge invariance remains in general an unwarranted assumption to be examined case by case. Armed with those modern tools, we reconsider here the classical Okubo–Marshak argument on the non-existence of a “strong CP problem” in quantum chromodynamics.

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Using methods of microlocal analysis, we prove that the regularization of divergent amplitudes stays a pure ultraviolet problem in string-localized field theories, despite the weaker localization. Thus, power counting does not lose its significance as an indicator for renormalizability. It also follows that standard techniques can be used to regularize divergent amplitudes in string-localized field theories.