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Alberto Castellano

Publications and source records attributed to Alberto Castellano.

18 recordsLinked to original sources
arXiv2026

How to (Non-)Perturb a BPS Black Hole

We relate the structure of non-perturbative corrections to BPS black hole observables in flat-spacetime theories with certain properties of probe charged particles in the near-horizon geometry. Concretely, we consider 4d $\mathcal{N} = 2$ supergravity with an infinite tower of F-terms and probe branes in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric-magnetic fields. The higher dimensional operators we pick are computed by Type II topological string theory, and we approximate them via the constant map contribution, which is valid at large volume and can be interpreted as arising from D0-branes integrated out in M-theory on a Calabi-Yau threefold times a circle. We analyze the resulting force conditions on massive particles carrying $(q_A, p^A)$ charges, their classical trajectories, and the 1-loop effective action they produce. A simple semiclassical analysis allows us to understand qualitatively the structure of the non-perturbative corrections. The exact path integral assessment then reproduces the Gopakumar--Vafa integral of the flat-spacetime theory, now evaluated in the black hole attractor geometry. Thus, we make explicit how the physics of the fully backreacted black hole solution is controlled by the behaviour of the light D-brane states which generate the relevant set of higher derivative corrections.

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arXiv2026

Exact Path Integral Methods in Supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ Backgrounds

We determine the exact functional determinants of charged, massive spin-0 and spin-$\frac12$ particles in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric and magnetic fields. This is achieved using Schwinger proper-time formalism, which allows us to derive the full non-perturbative effective action in the 1-loop and constant background field approximations. We then specialize the computation to supersymmetric settings and we obtain the effective action for a 4d $\mathcal{N}=2$ BPS massive hypermultiplet in a supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ spacetime. This setup can be seen to be equivalent to the near-horizon geometry of a BPS black hole which solves the attractor equations of 4d $\mathcal{N}=2$ supergravity. Our results provide a necessary intermediate step for the evaluation of the quantum-corrected black hole partition function. We also comment on the relation with the celebrated Gopakumar-Vafa integral representation.

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arXiv2026

Curvature divergences and gravity decoupling in Calabi--Yau rigid limits

Four-dimensional $\mathcal{N}=2$ supergravity theories become rigid in gravity-decoupling limits. We study this effect for type II string compactifications on general Calabi--Yau manifolds, focusing on vector-multiplet trajectories whose endpoints exhibit axionic shift symmetries. This comprises field excursions of both finite- and infinite distance, but the latter display specific features due to the appearance of light towers of extremal BPS states, in agreement with Swampland principles. We show that vector multiplets split into two sets: those with gravitational and with rigid mutual interactions, and that only a subset of the latter -- dubbed core RFT -- can fully decouple from gravity. We characterise the core RFT in terms of the axionic shift symmetry, and derive decoupling criteria based on kinetic and Pauli interaction mixing. Our framework is illustrated in large complex structure, conifold-like, and Seiberg--Witten limits. In the last case, Pauli mixing obstructs decoupling whenever the dyonic and extremal BPS towers appear at the same scale. Across all these examples, the decoupling from gravity is signalled by a divergent moduli-space scalar curvature.

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arXiv2025

On Supersymmetric D-brane probes in 4d $\mathcal{N}=2$ $\text{AdS}_2\times\mathbf{S}^2$ Attractors

We extend the $\kappa$-symmetry analysis of supersymmetric D-brane probes in the $\mathrm{AdS}_2 \times \mathbf{S}^2$ attractor geometry, originally performed by Simons, Strominger, Thompson, and Yin, to also include stationary -- but non-static -- worldlines carrying angular momentum along the 2-sphere. We demonstrate that certain special trajectories, with fixed radius and orbital velocity, solve the equations of motion and moreover satisfy a supersymmetry preserving condition, thus defining new $\frac12$-BPS configurations. Furthermore, these classical paths are shown to saturate a lower bound for the Hamiltonian generating global time translations, with the corresponding minimal energy depending on a generalized angular momentum vector $\boldsymbol{J}$. The direction of the latter, in turn, determines exactly which supercharges remain unbroken. Our results reveal a richer spectrum of (multi-particle) supersymmetric states in $\mathrm{AdS}_2 \times \mathbf{S}^2$, which can be organized into distinct selection sectors labeled by the conserved $SU(2)$ charges. This construction has direct applications in black hole microstate counting, the analysis of probe dynamics and $\text{AdS}_2/\text{CFT}_1$ holography.

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arXiv2025

Laplacians in Various Dimensions and the Swampland

The species cutoff is a moduli-dependent quantity signaling the onset of quantum gravitational phenomena, whose form can be oftentimes determined from higher-derivative and higher-curvature corrections within low-energy gravitational EFTs. In this work, we point out that these Wilson coefficients are eigenfunctions of an appropriate second-order elliptic operator defined over moduli space in theories with more than four supercharges. This was already known to be the case for the leading $\mathcal{R}^4$-correction to the two-derivative (bosonic) action of maximal supergravity in $d\leq 10$. Here, we reconsider this fact from the Swampland point of view and show how, in $d=10,9,8$, solving a Laplace equation imposes non-trivial restrictions on the species hull vectors. We further argue that this property is also satisfied in settings with less supersymmetry. In particular, we focus on the $\mathcal{R}^4$-operator in minimal supergravity theories in $d=10,9$, and on the leading $\mathcal{R}^2$-term in setups with 8 supercharges in $d=6,5,4$. Finally, we provide a symmetry-based criterion for determining when the relevant elliptic operator should be the Laplacian. A bottom-up rationale for this constraint remains to be fully understood, and we conclude by outlining some compelling possibilities.

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arXiv2025

Quantum Calabi-Yau Black Holes and Non-Perturbative D0-brane Effects

We compute the supersymmetric entropy of the most general BPS black hole in 4d $\mathcal{N}=2$ supergravity coupled to $n_V$ vector multiplets obtained from Type IIA string theory compactified on a Calabi-Yau threefold at large volume, including the all-genera leading-order $\alpha'$-corrections. These can be equivalently seen as D0-brane quantum effects from a dual five-dimensional M-theory perspective. We find that these corrections generically lead to both perturbative and non-perturbative contributions to the black hole entropy. We argue that the exception occurs for certain specific configurations where the gauge background, seen through the lens of D0-brane probes, behaves as purely electric or purely magnetic, thereby accounting for the absence of such non-perturbative effects. To explore this further, we perform a semiclassical analysis of the (non-)BPS particle dynamics in the near-horizon geometry of the underlying black hole, which is described by a maximally supersymmetric AdS$_2\times \mathbf{S}^2$ solution. As a byproduct, this study provides additional insights into the (non-perturbative) stability of supersymmetric black hole solutions and suggests an interpretation in terms of complex saddles contributing to the worldline path integral.

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arXiv2025

Black Hole Entropy, Quantum Corrections and EFT Transitions

We revisit and study quantum corrections to the supersymmetric entropy of BPS black holes in 4d $\mathcal{N}=2$ effective field theories (EFTs), which can be obtained from Type IIA string theory compactified on a Calabi-Yau threefold. Macroscopically, these corrections arise from an infinite series of higher-derivative F-terms that encode certain modifications to the two-derivative supergravity effective action. Within the large volume regime, we analyze in detail the moduli dependence of these semi-classical contributions and explore their implications for the black hole entropy. As a byproduct, we show that the entropy captures, in a rather intricate way, the transition between four- and five-dimensional dual EFT descriptions. In fact, the expansion parameter $\alpha$ controlling the relevant asymptotic series can be related to the ratio of the black hole horizon and the Kaluza-Klein scale, given here by the inverse D0-brane mass. Furthermore, we are able to resum the series into a well-behaved convergent expression for all values of $\alpha$. This demonstrates, in turn, that (stable) black holes can, indeed, probe scales besides the quantum gravity cutoff. More precisely, by examining two representative BPS systems -- the D0-D2-D4 and D2-D6 black hole solutions -- we explicitly illustrate how highly non-local (perturbative) quantum effects resolve the divergences, ultimately leading to a well-defined entropy function. Additionally, in certain cases, we show that one can take a suitable decompactification limit to 5d and verify that the corrected entropy function reproduces the exact microstate counting of the underlying five-dimensional black string. Our results also clarify the role of non-perturbative quantum corrections, which, remarkably, do not modify any of our prior conclusions.

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arXiv2025

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 $\textit{double EFT expansion}$ 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.

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arXiv2024

The Moduli Space Curvature and the Weak Gravity Conjecture

We unveil a remarkable interplay between rigid field theories (RFTs), charge-to-mass ratios $\gamma$ and scalar curvature divergences $\mathsf{R}_{\rm div}$ in the vector multiplet moduli space of 4d ${\cal N}=2$ supergravities, obtained upon compactifying type II string theory on Calabi--Yau threefolds. We show that the condition to obtain an RFT that decouples from gravity implies a divergence in the $\gamma$ of (would-be) BPS particles charged under the rigid theory, and vice-versa. For weak coupling limits, where the scalar curvature diverges, we argue that such BPS particles exist and that $\mathsf{R}_{\rm div} \lesssim \gamma^2$, implying that all these divergences are a consequence of RFT limits. More precisely, along geodesics we find that $\mathsf{R}_{\rm div} \sim (\Lambda_{\rm wgc}/\Lambda_g)^2$, where $\Lambda_{\rm wgc} \equiv g_{\rm rigid} M_{\rm Pl}$ is the RFT cut-off estimate of the Weak Gravity Conjecture and $\Lambda_g = g_{\rm rigid}^{-2} \Lambda_{\rm RFT}$ the electrostatic energy integrated up to its actual cut-off $\Lambda_{\rm RFT}$.

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arXiv2024

The Quantum Gravity Scale and the Swampland

This thesis investigates the role of the quantum gravity cut-off for effective field theories (EFTs) coupled to Einstein gravity, with an emphasis on its implications at low energies within the context of the Swampland program. Part I reviews the relevant aspects of string theory compactifications in different number of spacetime dimensions and with different amounts of supersymmetry preserved. In Part II a model-independent approach is employed so as to determine the maximum regime of validity of any such EFT, identifying the species scale as the natural candidate for the quantum gravity cut-off. We review various arguments proposed in the literature as well as include several new considerations on the matter. Part III provides a systematic study of this framework in string theory compactifications, yielding significant agreement with the previous perturbative and non-perturbative analysis. We also analyze various applications of this concept within the Swampland program, including the purported phenomenon of Emergence. Finally, in Part IV we explore the most immediate implications that this picture would have in the infrared regime, thus uncovering intriguing universal properties associated to the aforementioned energy scale, such as precise lower bounds on its exponential decay rates as well as certain patterns holding within the infinite distance corners of moduli space. The thesis includes new results scattered over the different chapters therein, which have not appeared in the author's original publications.

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arXiv2023

A Universal Pattern in Quantum Gravity at Infinite Distance

Quantum gravitational effects become significant at a cut-off species scale that can be much lower than the Planck scale whenever we get a parametrically large number of fields becoming light. This is expected to occur at any perturbative limit of an effective field theory coupled to gravity, or equivalently, at any infinite distance limit in the field space of the quantum gravity completion. In this note, we present a universal pattern that links the asymptotic variation rates in field space of the quantum gravity cut-off $\Lambda_{\text{sp}}$ and the characteristic mass of the lightest tower of states $m$: $\frac{\vec\nabla m}{m} \cdot\frac{\vec\nabla \Lambda_{\rm sp}}{ \Lambda_{\rm sp}}=\frac1{d-2}$, where $d$ is the spacetime dimension. This restriction can be used to make more precise several Swampland criteria that constrain the effective field theories that can be consistently coupled to quantum gravity.

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arXiv2023

Stringy Evidence for a Universal Pattern at Infinite Distance

Infinite distance limits in the moduli space of a quantum gravity theory are characterized by having infinite towers of states becoming light, as dictated by the Distance Conjecture in the Swampland program. These towers imply a drastic breakdown in the perturbative regimes of the effective field theory at a quantum gravity cut-off scale known as the species scale. In this paper, we find a universal pattern satisfied in all known infinite distance limits of string theory compactifications, which relates the variation in field space of the mass of the tower and the species scale: $\frac{\vec\nabla m}{m} \cdot\frac{\vec\nabla \Lambda_{\rm sp}}{ \Lambda_{\rm sp}}=\frac{1}{d-2}$ in $d$ spacetime dimensions. This implies a more precise definition of the Distance conjecture and sharp bounds for the exponential decay rates. We provide plethora of evidence in string theory and identify some sufficient conditions that allow the pattern to hold from a bottom-up perspective.

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arXiv2023

On the Species Scale, Modular Invariance and the Gravitational EFT expansion

The concept of the species scale as the quantum gravity cut-off has been recently emphasised in the context of the Swampland program. Along these lines, we continue the quest for a precise understanding of its role within effective field theories of gravity as well as a global definition of the latter in case there is enough supersymmetry preserved. To do so, we exploit duality symmetries, the familiar asymptotic dependence imposed by the presence of infinite towers of light states and the known behaviour of higher-curvature corrections to the Einstein-Hilbert action in various String Theory setups. In those cases, we obtain a self-consistent result for the identification of the species scale as the quantum gravity cut-off, but also present some puzzles related to the suppression of certain higher-dimensional operators as well as minor ambiguities that may arise in the deep interior of moduli space.

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arXiv2023

Entropy Bounds and the Species Scale Distance Conjecture

The Swampland Distance Conjecture (SDC) states that, as we move towards an infinite distance point in moduli space, a tower of states becomes exponentially light with the geodesic distance in any consistent theory of Quantum Gravity. Although this fact has been tested in large sets of examples, it is fair to say that a bottom-up justification that explains both the geodesic requirement and the exponential behavior has been missing so far. In the present paper we address this issue by making use of the Covariant Entropy Bound as applied to the EFT. When applied to backgrounds of the Dynamical Cobordism type in theories with a moduli space, we are able to recover these main features of the SDC. Moreover, this naturally leads to universal lower and upper bounds on the 'decay rate' parameter $\lambda_{\text{sp}}$ of the species scale, that we propose as a convex hull condition under the name of Species Scale Distance Conjecture (SSDC). This is in contrast to already proposed universal bounds, that apply to the SDC parameter of the lightest tower. We also extend the analysis to the case in which asymptotically exponential potentials are present, finding a nice interplay with the asymptotic de Sitter conjecture. To test the SSDC, we study the convex hull that encodes the (asymptotic) moduli dependence of the species scale. In this way, we show that the SSDC is the strongest bound on the species scale exponential rate which is preserved under dimensional reduction and we verify it in M-theory toroidal compactifications.

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arXiv2023

Towers and Hierarchies in the Standard Model from Emergence in Quantum Gravity

Based on Quantum Gravity arguments, it has been suggested that all kinetic terms of light particles below the UV cut-off could arise in the IR via quantum (loop) corrections. These loop corrections involve infinite towers of states becoming light (e.g. Kaluza-Klein or string towers). We study implications of this Emergence Proposal for fundamental scales in the Standard Model (SM). In this scheme all Yukawa couplings are of order one in the UV and small Yukawas for lighter generations appear via large anomalous dimensions induced by the towers of states. Thus, the observed hierarchies of quark and lepton masses are a reflection of the structure of towers of states that lie below the Quantum Gravity scale, $\Lambda_{\text{QG}}$. Small Dirac neutrino masses consistent with experimental observation appear due to the existence of a tower of SM singlet states of mass $m_{0}\simeq Y_{\nu_3}M_p\simeq 7\times 10^5$ GeV, opening up a new extra dimension, while the UV cut-off occurs at $\Lambda_{\text{QG}}\lesssim 10^{14}$ GeV. Additional constraints relating the Electro-Weak (EW) and cosmological constant (c.c.) scales (denoted $M_{\text{EW}}$ and $V_0$) appear if the Swampland condition $m_{\nu_1}\lesssim V_0^{1/4}$ is imposed (with $\nu_1$ denoting the lightest neutrino), which itself arises upon applying the AdS non-SUSY Conjecture or the AdS/dS Distance Conjecture to the 3d vacua from circle compactifications of the SM. In particular, the EW scale and that of the extra dimension fulfill ${m_0 \, M_{\text{EW}}\lesssim 10^{2}\, V_0^{1/4}M_p}$, thus relating the EW hierarchy problem to that of the c.c. Hence, all fundamental scales may be written as powers of the c.c., i.e. $m_{\bullet}\sim V_0^\delta M_p^{1-4\delta}$. The scale of SUSY breaking is $m_{3/2}\lesssim 7\times 10^5$ GeV, which favours a Mini-Split scenario that could be possibly tested at LHC and/or FCC.

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arXiv2022

The Emergence Proposal in Quantum Gravity and the Species Scale

In the Emergence Proposal in QG it is conjectured that all light-particle kinetic terms are absent in the fundamental UV theory and are generated by quantum corrections in the IR. It has been argued that this may provide for some microscopic understanding of the WGC and SDC. In the present paper we take the first steps towards a systematic study of Emergence in the context of string theory. We emphasize the crucial role of the species scale in any EFT coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of Emergence and show how kinetic terms for moduli, gauge bosons and fermions may be generated. One-loop computations play an important role in Emergence, so we present detailed calculations in $d$ spacetime dimensions for the wave-function renormalization of scalars, vectors and fermions. We extend and check the Emergence Proposal in a number string vacua, including 4d $\mathcal{N}=2$ theories arising from type IIA on a CY$_3$, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the emergence picture. Higher dimensional examples are also discussed, including 6d and 7d models arising from F-/M-theory on an elliptic CY$_3$ or a $K3$ surface. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from the emergence prescription, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini (and bosonic superpartners). Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in QG as an intrinsic IR phenomenon.

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arXiv2021

IR/UV Mixing, Towers of Species and Swampland Conjectures

By applying the Covariant Entropy Bound (CEB) to an EFT in a box of size $1/\Lambda_{\text{IR}}$ one obtains that the UV and IR cut-offs of the EFT are necessarily correlated. We argue that in a theory of Quantum Gravity (QG) one should identify the UV cutoff with the `species scale', and give a general algorithm to calculate it in the case of multiple towers becoming light. One then obtains an upper bound on the characteristic mass scale of the tower in terms of the IR cut-off, given by $M_{\text{tower}}\lesssim (\Lambda_{\text{IR}})^{2\alpha_D}$ in Planck units, with $\alpha_D=(D-2+p)/2p(D-1)$, where $p$ depends on the density of states. Identifying the IR cut-off with a (non-vanishing) curvature in AdS one reproduces the statement of the AdS Distance Conjecture (ADC), also giving an explicit lower bound for the $\alpha$ exponent. In particular, we find that the CEB implies $\alpha \geq1/2$ in any dimension if there is a single KK tower, both in AdS and dS vacua. However values $\alpha <1/2$ are allowed if the particle tower is multiple or has a string component. We also consider the CKN constraint coming from avoiding gravitational collapse which further requires in general $\alpha \geq 1/D$ for the lightest tower. We analyse the case of the DGKT-CFI class of Type IIA orientifold models and show it has both particle and string towers below the species scale, so that a careful analysis of how the ADC is defined is needed. We find that this class of models obey but do not saturate the CEB. The UV/IR constraints found apply to both AdS and dS vacua. We comment on possible applications of these ideas to the dS Swampland conjecture as well as to the observed dS phase of the universe.

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arXiv2021

A Gravitino Distance Conjecture

We conjecture that in a consistent supergravity theory with non-vanishing gravitino mass, the limit $m_{3/2}\rightarrow 0$ is at infinite distance. In particular one can write $M_{\mathrm{tower}} \sim m_{3/2}^\delta$ so that as the gravitino mass goes to zero, a tower of KK states as well as emergent strings becomes tensionless. This conjecture may be motivated from the Weak Gravity Conjecture as applied to strings and membranes and implies in turn the AdS Distance Conjecture. We test this proposal in classical 4d type IIA orientifold vacua in which one obtains a range of values $\tfrac13 \le \delta \le 1$. The parameter $\delta$ is related to the scale decoupling exponent in AdS vacua and to the $\alpha$ exponent in the Swampland Distance Conjecture for the type IIA complex structure. We present a general analysis of the gravitino mass in the limits of moduli space in terms of limiting Mixed Hodge Structures and study in some detail the case of two-moduli F-theory settings. Moreover, we obtain general lower bounds $\delta\, \geq \, \frac{1}{3}, \, \frac{1}{4}$ for Calabi--Yau threefolds and fourfolds, respectively. The conjecture has important phenomenological implications. In particular we argue that low-energy supersymmetry of order 1 TeV is only obtained if there is a tower of KK states at an intermediate scale, of order $10^8$ GeV. One also has an upper bound for the Hubble constant upon inflation $H \lesssim m_{3/2}^\delta M^{(1-\delta)}_{\text{P}}$.

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