Gravity-Induced Photon Interactions and Infrared Consistency in any Dimensions

TL;DR

This paper analyzes how gravity influences photon interactions across dimensions, deriving bounds on charged particles' properties, and explores implications for the Weak Gravity Conjecture and infrared consistency in effective field theories.

Contribution

It computes gravity-induced $F^4$ operators in any dimension, establishes positivity bounds from black hole and IR arguments, and connects these to the Weak Gravity Conjecture in various dimensions.

Findings

Positivity bounds constrain charge-to-mass ratios of heavy particles.

In $d=6$, beta functions of $F^4$ are positive, leading to WGC bounds with logarithmic enhancement.

In $d=9,10$, the WGC does not ensure extremal black hole decay, requiring large Planckian $F^4$ operators.

Abstract

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 $d\geq 4$) and from infrared (IR) consistency of four-photon scattering (for $d\geq 3$). 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.