Nontrivial zeros of the QED β-function (ultraviolet fixed points)

Determine whether the Gell-Mann–Low β-function of quantum electrodynamics possesses a nontrivial zero at finite coupling, thereby establishing or excluding the existence of a nontrivial ultraviolet fixed point for QED beyond perturbation theory.

Background

Gell-Mann and Low introduced the renormalisation group framework and highlighted the special role of zeros of the β-function as fixed points that govern high-energy behavior. They conjectured that the fine structure constant might correspond to such a fixed point.

However, beyond perturbation theory, the global behavior of the QED β-function is unknown, and in particular it is unknown whether it has any nontrivial (nonzero) zeros. Resolving this would clarify the ultraviolet completeness or triviality of QED.