Gravity-Induced Photon Interactions and Infrared Consistency in any Dimensions

We compute the four-photon ($F^4$) operators generated by loops of charged particles of spin $0$, $\frac{1}{2}$, $1$ in the presence of gravity and in any spacetime dimension $d$. To this end, we expand the one-loop effective action via the heat kernel coefficients, which capture both the gravity-induced renormalization of the $F^4$ operators and the low-energy Einstein-Maxwell effective field theory (EFT) produced by massive charged particles. We set positivity bounds on the $F^4$ operators using standard arguments from extremal black holes (for $d\ge 4$) and from infrared (IR) consistency of four-photon scattering (for $d\ge 3$). We find that both approaches yield nearly equivalent results, even though in the amplitudes we discard the graviton $t$-channel pole and use the vanishing of the Gauss-Bonnet term at quadratic order for any $d$. The positivity bounds constrain the charge-to-mass ratio of the heavy particles. If the Planckian $F^4$ operators are sufficiently small or negative, such bounds produce a version of the $d$-dimensional Weak Gravity Conjecture (WGC) in most, but not all, dimensions. In the special case of $d=6$, the gravity-induced beta functions of $F^4$ operators from charged particles of any spin are positive, leading to WGC-like bounds with a logarithmic enhancement. In $d=9,10$, the WGC fails to guarantee extremal black hole decay in the infrared EFT, thereby requiring the existence of sufficiently large Planckian $F^4$ operators.