The double EFT expansion in quantum gravity

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 double EFT expansion involving higher-curvature operators. The 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 quantum-gravitational expansion is suppressed relative to the Einstein-Hilbert term by the quantum gravity cutoff, \Lambda_{\text{QG}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mtext mathvariant="normal">QG</mml:mtext> </mml:msub> </mml:math> , above which no local gravitational EFT description remains valid. This structure becomes manifest in the so-called asymptotic regime, where a hierarchy between the Planck scale and \Lambda_{\text{QG}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>Λ</mml:mi> <mml:mtext mathvariant="normal">QG</mml:mtext> </mml:msub> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="script"> <mml:mi>𝒩</mml:mi> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> 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.