The Double EFT Expansion in Quantum Gravity

Abstract

In this work, we aim to characterize the structure of higher-derivative corrections within low-energy Effective Field Theories (EFTs) arising from a UV-complete theory of quantum gravity. To this end, we use string theory as a laboratory and argue that such EFTs should exhibit a $\textit{double EFT expansion}$ involving higher-curvature operators. The $\textit{field-theoretic}$ expansion is governed by the mass of the lightest (tower of) new degrees of freedom, as expected from standard field theory considerations. Conversely, the $\textit{quantum-gravitational}$ expansion is suppressed relative to the Einstein-Hilbert term by the quantum gravity cutoff, $\Lambda_{\rm QG}$, above which no local gravitational EFT description remains valid. This structure becomes manifest in the so-called $\textit{asymptotic regime}$, where a hierarchy between the Planck scale and $\Lambda_{\rm QG}$ emerges, the latter identified herein as the species scale. Most notably, we demonstrate the features of the double EFT expansion through an amplitudes-based approach in (toroidal compactifications of) ten-dimensional Type IIA string theory, and via a detailed analysis of the supersymmetric black hole entropy in 4d $\mathcal{N}=2$ supergravities derived from Type II Calabi-Yau compactifications. We provide further evidence for our proposal across various string theory setups, including Calabi-Yau compactifications of M/F-theory and Type II string theory. Finally, we explore the implications of this framework for the Wilson coefficients of the aforementioned higher-curvature operators, revealing potentially significant constraints in the asymptotic regime and highlighting a remarkable interplay with recent results from the S-matrix bootstrap program.