Ivano Basile: Asymptotic safety and the swampland

We propose testing the paradigm of asymptotically safe gravity using swampland conjectures. As a first step in this direction, we explore the infrared regime of asymptotically safe gravity in a toy model, quadratic gravity at one loop. We identify the hypersurface spanned by the endpoints of asymptotically safe renormalization group trajectories. These comprise the allowed values of higher-derivative couplings as well as standard logarithmic form factors. We determine the intersection of this hypersurface with the regions of parameter space allowed by the de Sitter conjecture, the trans-Planckian censorship conjecture and the weak gravity conjecture under the hypothesis of electromagnetic duality. The latter two depend on some order-one constants, for generic values of which we show that the overlap region is a proper subspace of the asymptotically safe hypersurface. Moreover, the latter lies inside the region allowed by the weak gravity conjecture. To conclude, we outline various extensions of this program, focusing on sharper bounds derived in the swampland and bootstrap literatures.