Application of positivity bounds in asymptotically safe gravity

Abstract

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.