Contributor info: Dr Alvaro Herraez

José Calderón-Infante, Alberto Castellano, Alvaro Herráez

SciPost Phys. 19, 096 (2025) · published 14 October 2025 | Toggle abstract · pdf

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, $\Lambda_{\text{QG}}$, 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 $\Lambda_{\text{QG}}$ 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.

Alvaro Herráez, Dieter Lüst, Joaquin Masias, Marco Scalisi

SciPost Phys. 18, 083 (2025) · published 6 March 2025 | Toggle abstract · pdf

Species thermodynamics has been proposed in analogy to black hole thermodynamics. The entropy scales like an area and is given by the mere counting of the number of the species. In this work, we derive the constitutive relations of species thermodynamics and explain how those originate from standard thermodynamics. We consider configurations of species in thermal equilibrium inside a box of size $L$, and show that the temperature $T$ of the system, which plays a crucial role, is always upper bounded above by the species scale $\Lambda_\mathrm{sp}$. We highlight three relevant regimes: (i) when $L^{-1}< T<\Lambda_\mathrm{sp}$, and gravitational collapse is avoided, the system exhibits standard thermodynamics features, for example, with the entropy scaling like the volume of the box; (ii) in the limit $L^{-1}\simeq T→ \Lambda_\mathrm{sp}$ we recover the rules of species thermodynamics with the entropy scaling like the area of the box; (iii) an intermediate regime with $ L^{-1}\simeq T< \Lambda_\mathrm{sp}$ that avoids gravitational collapse and fulfills the Covariant Entropy Bound; this interpolates between the previous two regimes and its entropy is given simply in terms of the counting of the species contributing to the thermodynamic ensemble. This study also allows us to find a novel and independent bottom-up rationale for the Emergent String Conjecture. Finally, we present the Black Hole - Tower Correspondence as a generalization of the celebrated Black Hole - String Correspondence. This provides us with a robust framework to interpret the results of our thermodynamic investigation. Moreover, it allows us to qualitatively account for the entropy of black holes in terms of the degrees of freedom of the weakly coupled species in the tower.