Unearthing the intersections: positivity bounds, weak gravity conjecture, and asymptotic safety landscapes from photon-graviton flows

We compute the asymptotic safety landscape stemming from ultraviolet-complete photon-graviton flows in a field theoretic setup, and we confront it with the weak gravity conjecture and, for the first time, with positivity bounds. At fourth order in derivatives, we find two gravitational fixed points providing viable ultraviolet completions for the theory. One of them comes with a single relevant direction, which sets the scale of quantum gravity. The corresponding sub-landscape is a single point. The second fixed point yields a richer sub-landscape of effective theories, most of which is described by an approximately straight line in the space of dimensionless Wilson coefficients. We additionally discover that: (i) the two sub-landscapes are continuously connected via a small "candy cane" regime, and the whole asymptotic safety landscape falls onto a plane; this is consistent with earlier findings and could be a universal feature in Asymptotic Safety; (ii) in such a field-theoretic setup, the Euler coupling plays a special role, as it is unconstrained by quantum scale invariance, but can enter off-shell bounds such as entropy-based positivity constraints; (iii) Planck-scale-suppressed violations of both weak gravity and positivity bounds occur across the landscape. The latter result resonates with expectations grounded on effective field theory arguments.