Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
Brando Bellazzini, Matthew Lewandowski, Javi Serra
TL;DR
The paper develops IR-safe positivity bounds for 4D theories containing a massless graviton by regulating the forward limit with a 3D cylinder compactification, subtracting gravity-induced KK and zero-mode effects to obtain a finite, positive dispersion relation for the $s^2$ coefficient of elastic amplitudes. Applied to the Einstein-Maxwell EFT, the bounds constrain higher-derivative operators $\alpha_i$, yielding $2\alpha_1-\alpha_3>0$, $2\alpha_1+\alpha_3>0$, and $\alpha_2>0$, which in turn modify extremality conditions and imply a mild form of the weak gravity conjecture: extremal black holes are self-repulsive and can decay to smaller extremal holes. The authors extend the analysis to scalars, axions, $P(X)$ theories, galileons, and curved spacetimes, finding that positivity bounds impose nontrivial UV-consistency constraints such as $\Lambda_{UV}\lesssim\mathrm{few}\times (H^3 m_{Pl})^{1/4}$ and that similar bounds can persist in de Sitter or anti-de Sitter backgrounds. Overall, the work connects fundamental S-matrix principles to concrete EFT constraints and black-hole physics, informing swampland considerations and guiding UV completion of gravity-coupled EFTs.
Abstract
We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that extremal black holes are self-repulsive, $M/|Q|<1$ in suitable units, and that they are unstable to decay to smaller extremal black holes, providing an S-matrix proof of the weak gravity conjecture. We also present other applications of our bounds to the effective field theory of axions, $P(X)$ theories, weakly broken galileons, and curved spacetimes.