We address the inverse problem in Type IIB flux compactifications of identifying flux vacua with targeted phenomenological properties such as specific superpotential values or tadpole constraints using conditional generative models. These machine learning techniques overcome computational bottlenecks in traditional approaches such as rejection sampling and Markov Chain Monte Carlo (MCMC), which struggle to generate rare, finely-tuned vacua. As a proof of concept, we demonstrate that conditional generative models provide a more efficient alternative, specifically using conditional variational autoencoders (CVAEs). We introduce a CVAE framework tailored to flux compactifications, incorporating physical constraints directly into the loss function — enabling the generation of physically consistent vacua beyond the training set. Our experiments on conifold and symmetric torus background geometries show that the CVAE achieves a speedup of about $$ \mathcal{O} $$ (10 ) compared to our KDE-based Metropolis baseline, particularly in narrow target ranges for superpotential values. Additionally, the CVAE generates novel, distinct flux configurations beyond the training data, highlighting its potential for probing computationally challenging regions of the string landscape. Our results establish conditional generative models as a promising tool for targeted flux vacua generation in the proof-of-concept geometries studied here, opening new pathways for model building in regions of the landscape previously inaccessible by traditional model building techniques.

United Kingdom

Sven Krippendorf

Zhimei Liu

Solving inverse problems of Type IIB flux vacua with conditional generative models

We uncover a new gravitational-wave production mechanism in cosmological, first-order, thermal phase transitions. These are usually assumed to proceed via the nucleation of bubbles of the stable phase inside the metastable phase. However, if the nucleation rate is sufficiently suppressed, then the Universe may supercool all the way down the metastable branch and enter the spinodal region. In this case the transition proceeds via the exponential growth of unstable modes and the subsequent formation, merging and relaxation of phase domains. We use holography to follow the real-time evolution of this process in a strongly coupled, four-dimensional gauge theory and compute the resulting gravitational-wave spectrum. We discuss the possibility that the spinodal dynamics may be preceded by a period of thermal inflation.

Spain

Finland

Yago Bea

Jorge Casalderrey-Solana

Portugal

Thanasis Giannakopoulos

Aron Jansen

Germany

David Mateos

Mikel Sanchez-Garitaonandia

Miguel Zilhão

Spinodal Gravitational Waves

We use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in ℙ4.

United States

Lara Anderson

Mathis Gerdes

James Gray

Nikhil Raghuram

CERN

Fabian Ruehle

Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning

We initiate a way of generating effective field theories (EFT) models by the computer, satisfying both experimental and theoretical constraints. We use Generative Adversarial Networks (GAN) and display generated instances which go beyond the examples known to the machine during training. As a starting point, we apply this idea to the generation of supersymmetric field theories with a single field. We find cases where the number of minima in the generated scalar potential is different from values found in the training data. We comment on potential further applications of this framework.

Harold Erbin

GANs for generating EFT models

We explore the possibility that (Bose-Einstein) condensation of scalar fields from string compactifications can lead to long-lived compact objects. Depending on the type of scalar fields we find different realisations of star-like and solitonic objects. We illustrate in the framework of type IIB string compactifications that closed string moduli can lead to heavy microscopic stars with masses of order  <math><msup><mi>V</mi><mi>α</mi></msup><msub><mi>M</mi><mi>Planck</mi></msub></math> $$ {\mathcal{V}}^{\alpha }{M}_{\mathrm{Planck}} $$, α = 1, 3/2, 5/3 where  <math><mi>V</mi></math> $$ \mathcal{V} $$ is the volume of the extra dimensions. Macroscopic compact objects from ultra-light string axions are realised with masses of order  <math><msup><mi>e</mi><mrow><mi>V</mi><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup></math> $$ {e}^{\mathcal{V}2/3} $$ M Planck . Q-ball configurations can be obtained from open string moduli whereas the closed string sector gives rise to a new class of solutions, named PQ-balls, that arise in the two-field axion-modulus system. The stability, the potential for the formation, and the observability of moduli stars through gravitational waves are discussed. In particular we point out that during the early matter phase given by moduli domination, density perturbations grow by a factor  <math><msup><mi>V</mi><mi>β</mi></msup></math> $$ {\mathcal{V}}^{\beta } $$ with β &gt; 2 and non-linear effects cannot be neglected.

Italy

Francesco Muia

Fernando Quevedo

Moduli stars

We argue that gravitational wave signals due to collisions of ultra-relativistic bubble walls may be common in string theory. This occurs due to a process of post-inflationary vacuum decay via quantum tunnelling. Though we study a specific string construction involving warped throats, we argue that our conclusions are more general. Many such transitions could have occurred in the post-inflationary Universe, as a large number of throats with exponentially different mass scales can be present in the string landscape, leading to several signals of widely different frequencies – a soundscape connected to the landscape of vacua. Detectors such as aLIGO/VIRGO, LISA, and pulsar timing observations with SKA and EPTA have the sensitivity to detect such signals. A distribution of primordial black holes is also a likely consequence, though reliable estimates of masses and their abundance require dedicated numerical simulations, as do the fine details of the gravitational wave spectrum due to the unusual nature of the transition.

Isabel Garcia Garcia

John March-Russell

The string soundscape at gravitational wave detectors

A generic feature of string compactifications is the presence of many scalar fields, called moduli. Moduli are usually displaced from their post-inflationary minimum during inflation. Their relaxation to the minimum could lead to the production of oscillons: localised, long-lived, non-linear excitations of the scalar fields. Here we discuss under which conditions oscillons can be produced in string cosmology and illustrate their production and potential phenomenology with two explicit examples: the case of an initially displaced volume modulus in the KKLT scenario and the case of a displaced blow-up Kähler modulus in the Large Volume Scenario (LVS). One, in principle, observable consequence of oscillon dynamics is the production of gravitational waves which, contrary to those produced from preheating after high scale inflation, could have lower frequencies, closer to the currently observable range. We also show that, for the considered parameter ranges, oscillating fibre and volume moduli do not develop any significant non-perturbative dynamics. Furthermore, we find that the vacua in the LVS and the KKLT scenario are stable against local overshootings of the field into the decompatification region, which provides an additional check on the longevity of these metastable configurations.

Switzerland

Stefan Antusch

Francesco Cefalà

Stefano Orani

Oscillons from string moduli

It is unknown whether a bound on axion field ranges exists within quantum gravity. We study axion field ranges using extended supersymmetry, in particular allowing an analysis within strongly coupled regions of moduli space. We apply this strategy to Calabi-Yau compactifications with one and two Kähler moduli. We relate the maximally allowable decay constant to geometric properties of the underlying Calabi-Yau geometry. In all examples we find a maximal field range close to the reduced Planck mass (with the largest field range being 3.25 M P ). On this perspective, field ranges relate to the intersection and instanton numbers of the underlying Calabi-Yau geometry.

Joseph Conlon

Axion decay constants away from the lamppost

In F-theory, U(1) gauge symmetries are encoded in rational sections, which generate the Mordell-Weil group of the elliptic fibration of the compactification space. Recently the possible U(1) charges for global SU(5) F-theory GUTs with smooth rational sections were classified [1]. In this paper we utilize this classification to probe global F-theory models for their phenomenological viability. After imposing an exotic-free MSSM spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the presence of U(1) gauge symmetries), absence of dimension four and five proton decay operators and other R-parity violating couplings, and the presence of at least the third generation top Yukawa coupling, we generate the remaining quark and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we require that the dangerous couplings are forbidden at leading order, and when re-generated by singlet vevs, lie within the experimental bounds. We scan over all possible configurations, and show that only a small class of U(1) charge assignments and matter distributions satisfy all the requirements. The solutions give rise to the exact MSSM spectrum with realistic quark and lepton Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We also discuss the geometric realization of these models, and provide pointers to the class of elliptic fibrations with good phenomenological properties.

Sakura Schäfer-Nameki

Jin-Mann Wong

Froggatt-Nielsen meets Mordell-Weil: a phenomenological survey of global F-theory GUTs with U(1)s

We study the phenomenology of the CMSSM/mSUGRA with non-thermal neutralino dark matter. Besides the standard parameters of the CMSSM we include the reheating temperature as an extra parameter. Imposing radiative electroweak symmetry breaking with a Higgs mass around 125 GeV and no dark matter overproduction, we contrast the scenario with different experimental bounds from colliders (LEP, LHC), cosmic microwave background (Planck), direct (LUX, XENON100, CDMS, IceCube) and indirect (Fermi) dark matter searches. The allowed parameter space is characterised by a Higgsino-like LSP with a mass around 300 GeV. The observed dark matter abundance can be saturated for reheating temperatures around 2GeV while larger temperatures require extra non-neutralino dark matter candidates and extend the allowed parameter space. Sfermion and gluino masses are in the few TeV region. These scenarios can be achieved in string models of sequestered supersymmetry breaking which avoid cosmological moduli problems and are compatible with gauge coupling unification. Astrophysics and particle physics experiments will fully investigate this non-thermal scenario in the near future.