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The Double EFT Expansion in Quantum Gravity
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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.
Forward citations
Cited by 10 Pith papers
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Kaluza-Klein tower thresholds and scheme dependence of the species scale
Leading KK-tower local corrections to four-derivative gravity are regulator-dependent EFT matching data, while log N terms are universal within proper-time cutoffs, so species-scale definitions match only parametrically.
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IR Black Hole Instabilities Trigger Species-Scale Particle Production
A mechanism is proposed in which black hole instability at the tower scale converts a fraction of the mass into particles at the species scale, with Hawking evaporation subdominant.
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Minimal classical BPS black holes in string compactifications track the species or KK scale in infinite-distance limits, and violations may signal inconsistent EFTs.
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DESI data indicating evolving dark energy may allow string theory to describe observed universes without violating swampland constraints on constant dark energy.
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A short overview on the Black Hole-Tower Correspondence and Species Thermodynamics
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