arXiv subjects

Gonzalo F. Casas

Publications and source records attributed to Gonzalo F. Casas.

10 recordsLinked to original sources

arXiv2026

Gravity Decoupling and Axionic Shift Symmetries

We analyse the rôle of approximate axionic shift symmetries in gravity-decoupling limits arising in type II Calabi-Yau compactifications. Associated with each shift symmetry there is an axionic string whose tension constrains the gradient of the Kähler potential, as expected in regimes where gravity becomes weakly coupled. The gradients of these tensions define vector fields on moduli space, analogous to those associated with BPS particle masses. Together, they characterise the evolution of different effective field theory sectors along asymptotic limits, encoding both their coupling to gravity and their kinetic mixing. By deriving upper bounds on the inner products of these vector fields, we show that they split into mutually orthogonal subsets, one of which decouples from gravity. Finally, we relate the Laplacian of certain axionic string tensions to a divergent moduli space curvature.

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arXiv2026

Towards the Non-Perturbative Completion of 4d N=1 Effective Theories of Gravity

We show that four-dimensional $\mathcal N=1$ effective theories of gravity obtained from string compactifications require a non-perturbative completion, as additional light states of non-perturbative origin must be incorporated in the small volume regime to obtain a consistent low-energy description. This completion becomes concrete in subsectors that locally exhibit enhanced supersymmetry, where the enhancement predicts the existence of additional light degrees of freedom absent in the perturbative description. Motivated by analogous setups in six-dimensional $\mathcal N=(1,0)$ theories, we focus on the Kähler moduli space of F-theory compactifications on Calabi--Yau fourfolds to four dimensions, where shrinkable curves not intersected by 7-planes realize such supersymmetry-enhanced subsectors. Guided by the enhanced supersymmetry, we use F-theory to identify the degrees of freedom missing in the small volume regime of the perturbative Type IIB description. A consistent embedding of these local subsectors into a four-dimensional $\mathcal N=1$ theory of gravity requires an appropriate inclusion of complex structure moduli and spacetime-filling D3-branes. We also discuss supersymmetry enhancement in the complex structure sector and study how a heterotic dual description gives a unifying picture of the different F-theory sectors with enhanced supersymmetry. Finally, we comment on cases without local supersymmetry enhancement.

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arXiv2025

Moduli Self-Fixing

In Quantum Gravity (QG), large moduli values lead to towers of exponentially light states, making the QG cut-off field-dependent. In 4D supersymmetric (SUSY) theories, this cut-off is set by the species scale $Λ(z_i, \bar{z}_i)$, where $z_i$ are complex moduli. We argue that in GKP-like 4D no-scale vacua, accounting for this field dependence generates one-loop, positive-definite potentials for the otherwise unfixed moduli, with local Minkowski minima at the desert points in moduli space with $z_i \sim \mathcal{O}(1)$. As these no-scale moduli grow, a dS plateau emerges and, for larger moduli, the potential runs away to zero, consistent with Swampland expectations. This may have important consequences for the moduli fixing problem. In particular non-perturbative superpotentials may not be necessary for fixing the Kähler moduli in a Type IIB setting. Although one loses control over non-perturbative corrections, we argue that modular invariance (more generally, dualities) of the species scale may give us information about the behaviour at small moduli in some simple cases. We illustrate this mechanism in a Type II 4D $\mathbb{Z}_2 \times \mathbb{Z}_2$ toroidal orientifold, where in some cases, modular invariance can give us control over the non-perturbative corrections. The vanishing cosmological constant reflects a delicate cancellation between IR and UV contributions at the minimum. The models may be completed by the addition of intersecting D6-branes, yielding a 3-generation MSSM (RR tadpole free) model with some (but not all) closed string moduli fixed in Minkowski, with the complex structure moduli fixed at the desert points.

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arXiv2025

Cosmology of light towers and swampland constraints

We study the dynamical evolution of FLRW cosmologies in the presence of a tower of scalar light states and a runaway exponential potential. Some of the attractor solutions have problematic behaviours from the EFT point of view, which we use to argue for restrictions on the possible exponential scalings of the potential and tower characteristic mass as we move towards asymptotic regions in moduli space. These serve as further evidence that the tower mass should not decay faster than the potential or the KK scale associated to the homogeneous decompactification of a single compact dimension. We provide support from different top-down compactifications and connect with previous arguments found in the literature.

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arXiv2024

Modular Invariant Starobinsky Inflation and the Species Scale

Potentials in cosmological inflation often involve scalars with trans-Planckian ranges. As a result, towers of states become massless and their presence pushes the fundamental scale not to coincide with $M_{\rm P}$ but rather with the $species\, scale$, $Λ$. This scale transforms as an automorphic form of the theory's duality symmetries. We propose that the inflaton potential should be 1) an automorphic invariant form, non-singular over all moduli space, 2) depending only on $Λ$ and its field derivatives, and 3) approaching constant values in the large moduli to ensure a long period of inflation. These conditions lead to the proposal $V \sim λ(ϕ, ϕ^*)$, with $λ= G^{i\bar{j}} (\partial_i Λ)(\partial_{\bar{j}} Λ) / Λ^2$, determining the 'species scale convex hull'. For a single elliptic complex modulus with $SL(2, Z)$ symmetry, this results in an inflaton potential $V \simeq (\text{Im} τ)^2 |\tilde{G}_2|^2 / N^2$, with $N \simeq -\log(\text{Im} τ|η(τ)|^4)$, where $η$ is the Dedekind function and $\tilde{G}_2$ the Eisenstein modular form of weight 2. Surprisingly, this potential at large modulus resembles that of the Starobinsky model. We compute inflation parameters yielding results similar to Starobinsky's, but extended to modular invariant expressions. Interestingly, the number of e-folds is proportional to the number of species in the tower, $N_e \simeq N$, and $ε\simeq Λ^4$ at large moduli, suggesting that the tower of states plays an important role in the inflation process.

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arXiv2024

Yukawa Couplings at Infinite Distance and Swampland Towers in Chiral Theories

We study limits of vanishing Yukawa couplings of 4d chiral matter fields in Quantum Gravity, using as a laboratory type IIA orientifolds with D6-branes. In these theories chiral fermions arise at brane intersections, where an infinite tower of charged particles dubbed gonions are localised. We show that in the limit $Y\rightarrow 0$ some of these towers become asymptotically massless, while at the same time the kinetic term of some chiral fields becomes singular and at least two extra dimensions decompactify. For limits parametrised by a large complex structure saxion $u$, Yukawa couplings have a behaviour of the form $Y \, \sim \, {1}/{u^r}$, with $r$ some positive rational number. Moreover, in this limit some of the gauge couplings associated to the Yukawa vanish. The lightest gonion scales are of order $m_{\rm gon} \sim g^s M_{\rm P}$ with $s>1$, verifying the magnetic WGC with room to spare and with no need of its tower/sublattice versions. We also show how this behaviour can be understood in the context of the emergence of kinetic terms in Quantum Gravity. All these results may be very relevant for phenomenology, given the fact that some of the Yukawa couplings in the Standard Model are very small.

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arXiv2024

On small Dirac Neutrino Masses in String Theory

We study how tiny Dirac neutrino masses consistent with experimental constraints can arise in string theory SM-like vacua. We use as a laboratory 4d ${\cal N}=1$ type IIA Calabi--Yau orientifold compactifications, and in particular recent results on Yukawa couplings at infinite field-space distance. In this regime we find Dirac neutrino masses of the form $m_ν\simeq g_ν\langle H\rangle$, with $g_ν$ the gauge coupling of the massive $U(1)$ under which the right-handed neutrinos $ν_R$ are charged, and which should be in the range $g_ν\simeq 10^{-14}-10^{-12}$ to reproduce neutrino data. The neutrino mass suppression occurs because the right-handed neutrino kinetic term behaves as $K_{νν} \simeq 1 /g_ν^2 $. At the same time a tower of $ν_R$-like states appears with characteristic scale $m_0\simeq g_ν^2M_{\rm P}\simeq 0.1-500$ eV, in agreement with Swampland expectations. Two large hidden dimensions only felt by the $ν_R$ sector arise at the same scale, while the string scale is around $M_s\simeq g_νM_{\rm P}\simeq 10-700$ TeV. Some phenomenological implications and model building challenges are described. As a byproduct, independently of the neutrino issue, we argue that a single large dimension in the context of SM-like type IIA Calabi--Yau orientifolds leads to too small Yukawa couplings for quarks and charged leptons.

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arXiv2024

Cosmological Chameleons, String Theory and the Swampland

We study a scenario with a transient phase of cosmological acceleration that could potentially be realized in asymptotic corners of String Theory moduli space. A very steep scalar potential is temporarily stabilized by the effect of a nonzero density of heavy states, leading to acceleration, in what amounts to a cosmological version of the Chameleon mechanism. The density of heavy states is diluted by cosmological expansion, weakening their effect. After roughly one $e$-fold their effect can no longer stabilize the potential, and the accelerating phase ends. We also study a scenario where there is no potential and the transient acceleration is achieved by the counterbalancing effects of light and heavy towers of states. In both cases we show that it is not possible to obtain more than $\mathcal{O}(1)$ $e$-folds without transplanckian field excursions. We also discuss the general EFT constraints on these models and explore a number of first attempts at concrete embeddings of the scenario in String Theory. These all turn out to face significant challenges.

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arXiv2023

Torsion in cohomology and dimensional reduction

Conventional wisdom dictates that $\mathbb{Z}_N$ factors in the integral cohomology group $H^p(X_n, \mathbb{Z})$ of a compact manifold $X_n$ cannot be computed via smooth $p$-forms. We revisit this lore in light of the dimensional reduction of string theory on $X_n$, endowed with a $G$-structure metric that leads to a supersymmetric EFT. If massive $p$-form eigenmodes of the Laplacian enter the EFT, then torsion cycles coupling to them will have a non-trivial smeared delta form, that is an EFT long-wavelength description of $p$-form currents of the $(n-p)$-cycles of $X_n$. We conjecture that, whenever torsion cycles are calibrated, their linking number can be computed via their smeared delta forms. From the EFT viewpoint, a torsion factor in cohomology corresponds to a $\mathbb{Z}_N$ gauge symmetry realised by a Stückelberg-like action, and calibrated torsion cycles to BPS objects that source the massive fields involved in it.

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arXiv2022

Membranes in AdS4 orientifold vacua and their Weak Gravity Conjecture

We study type IIA orientifold compactifications with fluxes that give rise to perturbatively stable, non-supersymmetric AdS$_4$ vacua with D6-brane gauge sectors. Non-perturbative instabilities can be mediated by D8-branes wrapped on the six internal dimensions $X_6$, if they reduce to 4d membranes with a charge $Q$ larger than its tension $T$. The mismatch $Q \neq T$ arises due to i) curvature corrections and ii) the BIon backreaction of D6-branes wrapping 3-cycles of $X_6$. We give a simple expression for the second effect in toroidal orientifolds, and find that only pairs of 3-cycles at SU(2) angles contribute to it. They either contribute towards $Q>T$ or $Q<T$ depending on the 3-cycles separation, allowing to engineer 4d $\mathcal{N}=0$ vacua in tension with the Weak Gravity Conjecture for membranes.

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