  Positivity bounds are bounds on the Wilson coefficients of an effective field
theory. They hold, if the ultraviolet completion satisfies unitarity,
microcausality, locality and Lorentz symmetry; accordingly their violation
signals a violation of at least one of these properties of the ultraviolet
completion. We explore whether positivity bounds on four-photon-couplings hold,
when the ultraviolet completion is an asymptotically safe gravity-photon
theory. By working at sixth order in an expansion in the electromagnetic field
strength, we discover indications that positivity bounds hold for effective
field theories that are UV completed by the asymptotically safe Reuter fixed
point. We also perform various tests of the robustness of our result. This
amounts to a nontrivial and critical indication of the physical viability of
asymptotically safe gravity.
