We develop tools of Bayesian inference on the moduli space of Calabi–Yau (CY) manifolds. We sample from the invariant Weil–Petersson (WP) measure using Markov Chain Monte Carlo and normalizing flows on Kähler moduli space with dimension up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>h</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup><mo>=</mo><mn>30</mn></math>, and present results on the spectrum of the CY volume and properties of divisors when the measure is restricted in physically meaningful ways. We furthermore present a theory-informed prior on axion masses and decay constants <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><msub><mi>m</mi><mi>a</mi></msub><mo>,</mo><msub><mi>f</mi><mi>a</mi></msub><mo stretchy="false">)</mo></math> marginalized over the WP measure for all inequivalent CYs constructable from the Kreuzer–Skarke database with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>h</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup><mo>≤</mo><mn>5</mn></math>. We then impose likelihoods based on axion physics. We demonstrate how detection of a relatively heavy QCD axion at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>h</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math>, e.g., by the Axion Dark Matter Experiment, provides detailed information about CY geometry and topology. Finally, we compute a full forward model incorporating likelihoods from the cosmic microwave background and Lyman-alpha forest and find the maximum posterior probability region on the moduli space of a given CY favored by a resolution of the tension in these data by an ultralight axion composing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo>%</mo><mo stretchy="false">)</mo></math> of the dark matter. This demonstration serves as a blueprint for future statistical analyses within string phenomenology.

United Kingdom

United States

Mudit Jain

Elijah Sheridan

David J.E. Marsh

Elli Heyes

Keir K. Rogers

Germany

Andreas Schachner

Bayesian inference on Calabi-Yau moduli spaces and the axiverse: Experimental data meets string theory

We analyse warping corrections to the scalar potential in flux compactifications of Type IIB string theory, focusing on their effect on $\textit{F}$-term de Sitter uplifting in Calabi-Yau orientifold models. A systematic inverse-volume expansion allows us to derive the four-dimensional off-shell potential in the presence of warping and non-ISD 3-form fluxes. This corresponds to integrating out all massive Kaluza-Klein modes using the ten-dimensional equations of motion. We further propose a warped Kähler potential in four-dimensional 𝒩 = 1 supergravity, and show that it is consistent with our ten-dimensional results. In the KKLT framework, we find that classical warping corrections, as well as mixed corrections involving non-ISD fluxes and quantum effects, are dominant, rendering the scenario effectively uncontrollable with current methods. By contrast, in LVS-like constructions these corrections are suppressed by inverse powers of the volume, specifically 𝒱 or 𝒱 , depending on the concrete model.

Arthur Hebecker

France

Severin Lüst

Simon Schreyer

Effective potentials, warping, and implications for $\textit{F}$-term uplifting

We present a comprehensive study of Kähler moduli stabilisation in Type IIB flux compactifications, combining advanced numerical techniques with analytical methods. Our JAX-based computational framework enables efficient scanning of the UV parameter space, while incorporating $\textit{α}$ corrections, loop and non-perturbative effects, as well as uplift contributions to the scalar potential. The implementation features rigorous vacuum validation protocols derived from analytic results. We apply our methods to explicit flux compactifications on more than 80,000 Calabi-Yau threefolds with $\textit{h}$ ≤ 6 Kähler moduli. By systematically scanning over a wide range of values of the flux superpotential $\textit{W}$ and the string coupling $\textit{g}$ , we find explicit realisations of every established Kähler moduli stabilisation scenario: for 10 ≤ |$\textit{W}$ | ≤ 10 we obtain both KKLT-like and Kähler uplifted vacua, while for the broader range 10 ≤ |$\textit{W}$ | ≤ 10 we recover LVS as well as LVS-like hybrid solutions. Notably, we discover significant parameter regions where multiple vacua coexist within a single flux potential, including novel configurations pairing AdS, Minkowski, and dS minima with different volume hierarchies. These findings enable, for the first time, the analysis of vacuum decay processes within fixed flux configurations, complementing the established theory of transitions between distinct flux vacua and decays towards decompactification.

Iran

Shehu AbdusSalam

Christopher Hughes

not found

Fernando Quevedo

Coexisting flux string vacua from numerical Kähler moduli stabilisation

We study the Type IIB eight-derivative effective Lagrangian beyond the quartic level, focusing on interactions involving gravitons and axio-dilatons. We show how to translate five-point scattering amplitudes into genuine five-point contact terms and extract all perturbative contributions to the effective action. Our result is consistent with T-duality predictions at tree level in the NSNS sector. We find that couplings with an even/odd number of scalars are neutral/charged under SL(2, $\textit{ℤ}$), and use this feature to deduce their non-perturbative completion. The mixed NSNS/RR structures that cannot be deduced from the pure NSNS sector allow us to unambiguously fix the kinematics, which turns out to be the same for tree level and one loop. In Type IIA, these structures are essential for establishing agreement of string-theoretic corrections with the circle reduction of M-theory higher-derivative couplings.

James Liu

Ruben Minasian

Italy

Raffaele Savelli

Type IIB at eight derivatives: five-point axio-dilaton couplings

We study fuzzy axion dark matter in type IIB string theory, for axions descending from the Ramond-Ramond four-form in compactifications on orientifolds of Calabi-Yau hypersurfaces. Such models can be tested by cosmological measurements if a significant relic abundance of fuzzy dark matter arises, which we argue is most common in models with small numbers of axions. We construct a topologically exhaustive ensemble of more than 350,000 Calabi-Yau compactifications yielding up to seven axions, and in this setting we perform a systematic analysis of misalignment production of fuzzy dark matter. In typical regions of moduli space, the fuzzy axion, the QCD axion, and other axions have comparable decay constants of $\textit{f}$ ≈ 10 GeV. We find that overproduction of heavier axions is problematic, except at special loci in moduli space where decay constant hierarchies can occur: without a contrived reheating epoch, it is necessary to fine-tune initial displacements. The resulting dark matter is typically a mix of fuzzy axions and heavier axions, including the QCD axion. Dark photons are typically present as a consequence of the orientifold projection. We examine the signatures of these models by simulating halos with multiple fuzzy axions, and by computing new cosmological constraints on ultralight axions and dark radiation. We also give evidence that cosmic birefringence is possible in this setting. Our findings determine the phenomenological correlates of fuzzy axion dark matter in a corner of the landscape.

Federico Carta

Naomi Gendler

David Marsh

Liam McAllister

Nicole Righi

Canada

Keir Rogers

Fuzzy axions and associated relics

With the discovery of a Higgs boson with a mass of 125 gigaelectronvolts (GeV) at the Large Hadron Collider (LHC) at CERN in 2012, the Standard Model (SM) is complete, and despite intensive searches, no new fundamental particle has been observed since then. In fact, a discovery can be challenging without a predictive new physics model because different channels and observables cannot be combined directly and unambiguously. Furthermore, without supporting indirect hints, the signal space to be searched is huge, resulting in diluted significances owing to the look-elsewhere effect. Several LHC processes with multiple leptons in the final state point towards the existence of a new Higgs boson with a mass between 140 GeV to 160 GeV decaying mostly to $\textit{W}$ bosons. While the former strongly reduces the look-elsewhere effect, the latter indicates that it could be a Higgs triplet with zero hypercharge. Within this simple and predictive extension of the SM, we simulate and combine different channels of di-photon production in association with leptons, missing energy, jets, $\textit{etc}$... Using the full run-2 results by ATLAS, including those presented recently at the Moriond conference, an increased significance of 4 standard deviations is obtained for a $\approx$ 152 GeV Higgs. Due to the previously predicted mass range, the look-elsewhere effect is negligible, and this constitutes the highest statistical evidence for a new narrow resonance obtained at the LHC. Furthermore, the model predicts a heavier-than-expected $\textit{W}$ boson, as indicated by the global electroweak fit. If further substantiated, the discovery of a new Higgs would overthrow the SM, provide a compelling case for the construction of future particle colliders, and pave the way to a novel understanding of the known shortcomings of the SM. In particular, the triplet Higgs field can lead to a strong first-order phase transition and could thus be related to the matter anti-matter asymmetry in our Universe.

Switzerland

Andreas Crivellin

China

Saiyad Ashanujjaman

Sumit Banik

Guglielmo Coloretti

India

Siddharth P. Maharathy

South Africa

Bruce Mellado

Growing evidence for a Higgs triplet * The work of Andreas Crivellin is supported by a Professorship Grant from the Swiss National Science Foundation (PP00P21_76884). The work of Saiyad Ashanujjaman is partially supported by the National Natural Science Foundation of China (11835013). Siddharth P. Maharathy acknowledges using the SAMKHYA: High-Performance Computing Facility provided by the Institute of Physics, Bhubaneswar

We construct compactifications of type IIB string theory that yield, at leading order in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>α</mi><mo>′</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mi>s</mi></msub></math> expansions, de Sitter vacua of the form envisioned by Kachru et al. We specify explicit Calabi-Yau orientifolds and quantized fluxes for which we derive the four-dimensional effective supergravity theories, incorporating the exact flux superpotential, the nonperturbative superpotential from Euclidean D3-branes, and the Kähler potential at tree level in the string loop expansion but to all orders in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>α</mi><mo>′</mo></msup></math>. Each example includes a Klebanov-Strassler throat region containing a single anti-D3-brane, whose supersymmetry-breaking energy, computed at leading order in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>α</mi><mo>′</mo></msup></math>, causes an uplift to a metastable de Sitter vacuum in which all moduli are stabilized. Finding vacua that demonstrably survive subleading corrections, and in which the quantization conditions are completely understood, is an important open problem for which this work has prepared the foundations.

CERN

Jakob Moritz

Richard Nally

Candidate de Sitter vacua

We study the non-linear structure of Type IIB eight-derivative couplings involving the metric and the complexified three-form G 3. We show that, at the level of five-point string amplitudes, the kinematics in the maximally R-symmetry-violating sector is fully matched by standard superspace integrals and by superparticle amplitudes in M-theory on a two-torus. The latter approach is used to determine the complete effective action in this sector and to verify its invariance under SL(2, ℤ) duality. We further comment on the general structure of the higher-point kinematics. Compactifications to lower dimensions provide both tests for our results and the arena for their applications. We verify that K3 reductions are fully consistent with the constraints of six-dimensional supersymmetry, and derive the four-dimensional flux scalar potential and axion kinetic terms at order (α′)3 in Calabi-Yau threefold reductions.

Type IIB at eight derivatives: insights from Superstrings, Superfields and Superparticles

The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star triangulations (FRSTs). Until now, the vastness of this geometric landscape remains largely unexplored. In this paper, we construct Calabi-Yau orientifolds from holomorphic reflection involutions of such hypersurfaces with Hodge numbers h 1,1 ≤ 12. In particular, we compute orientifold configurations for all favourable FRSTs for h 1,1 ≤ 7, while randomly sampling triangulations for each pair of Hodge numbers up to h 1,1 = 12. We find explicit string compactifications on these orientifolded Calabi-Yaus for which the D3-charge contribution coming from Op-planes grows linearly with the number of complex structure and Kähler moduli. We further consider non-local D7-tadpole cancellation through Whitney branes. We argue that this leads to a significant enhancement of the total D3-tadpole as compared to conventional SO(8) stacks with (4 + 4) D7-branes on top of O7-planes. In particular, before turning-on worldvolume fluxes, we find that the largest D3-tadpole in this class occurs for Calabi-Yau threefolds with <math> <mfenced> <msubsup> <mi>h</mi> <mo>+</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>h</mi> <mo>−</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msubsup> </mfenced> </math> $$ \left({h}_{+}^{1,1},{h}_{-}^{1,2}\right) $$ = (11, 491) with D3-brane charges |Q D3 | = 504 for the local D7 case and |Q D3 | = 6, 664 for the non-local Whitney branes case, which appears to be large enough to cancel tadpoles and allow fluxes to stabilise all complex structure moduli. Our data is publicly available under the following link https://github.com/AndreasSchachner/CY_Orientifold_database .

Chiara Crinò

Roberto Valandro

A database of Calabi-Yau orientifolds and the size of D3-tadpoles

Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms (B 2 , C 2) in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D <math> <mi>N</mi> </math> $$ \mathcal{N} $$ = 1 F-term scalar potentials at higher orders in the α′ and g s expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of (α′)3 corrections to the Kähler potential. By studying a partially SL(2, ℤ)-completed form of the Kähler potential, we derive the exact no-scale breaking effects at the closed string 1-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the F-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.

Michele Cicoli

Pramod Shukla

Systematics of type IIB moduli stabilisation with odd axions