Moduli Fields Research Articles

Modulus stabilization in the multiple-modulus framework

In a class of modular-invariant models with multiple moduli fields, the viable lepton flavor mixing pattern can be realized if the values of moduli are selected to be at the fixed points. In this paper, we investigate a modulus stabilization mechanism in the multiple-modulus framework which is capable of providing de Sitter (dS) minima precisely at the fixed points τ=i and ω, by taking into consideration nonperturbative effects on the superpotential and the dilaton Kähler potential. Due to the existence of additional Kähler moduli, more possible vacua can occur, and the dS vacua could be the deepest under certain conditions. We classify different choices of vacua and discuss their phenomenological implications for lepton masses and flavor mixing. Published by the American Physical Society 2024

Modular invariant slow roll inflation

We propose new classes of inflation models based on the modular symmetry, where the modulus field τ serves as the inflaton. We establish a connection between modular inflation and modular stabilization, wherein the modulus field rolls towards a fixed point along the boundary of the fundamental domain. We find the modular symmetry strongly constrain the possible shape of the potential and identify some parameter space where the inflation predictions agree with cosmic microwave background observations. The tensor-to-scalar ratio is predicted to be smaller than 10-6 in our models, while the running of spectral index is of the order of 10-4.

Probing SUSY at gravitational wave observatories

Under the assumption that the recent pulsar timing array evidence for a stochastic gravitational wave (GW) background at nanohertz frequencies is generated by metastable cosmic strings, we analyze the potential of present and future GW observatories for probing the change of particle degrees of freedom caused, e.g., by a supersymmetric (SUSY) extension of the Standard Model (SM). We find that signs of the characteristic doubling of degrees of freedom predicted by SUSY could be detected at Einstein Telescope and Cosmic Explorer even if the masses of the SUSY partner particles are as high as about 104 TeV, far above the reach of any currently envisioned particle collider. We also discuss the detection prospects for the case that some entropy production, e.g. from a late decaying modulus field inducing a temporary matter domination phase in the evolution of the universe, somewhat dilutes the GW spectrum, delaying discovery of the stochastic GW background at LIGO-Virgo-KAGRA. In our analysis we focus on SUSY, but any theory beyond the SM predicting a significant increase of particle degrees of freedom could be probed this way.

Wormholes in the axiverse, and the species scale

We analyze a large class of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 low-energy realizations of the axiverse satisfying various quantum gravity constraints. We propose a novel upper bound on the ultimate UV cutoff of the effective theory, namely the species scale, which only depends on data available at the two-derivative level. Its dependence on the moduli fields and the number N of axions matches expectations from other independent considerations. After an assessment of the regime of validity of the effective field theory, we investigate the non-perturbative gravitational effects therein. We identify a set of axionic charges supported by extremal and non-extremal wormhole configurations. We present a universal class of analytic wormhole solutions, explore their deformations, and analyze the relation between wormhole energy scales and the species scale. The connection between these wormholes and a special subclass of BPS fundamental instantons is discussed, and an argument in favor of the genericity of certain axion-dependent effective superpotentials is provided. We find a lower bound increasing with N ≫ 1 on the Gauss-Bonnet coefficient, resulting in an exponential suppression of non-extremal wormhole effects. Our claims are illustrated and tested in concrete string theory models.

Modular invariant hilltop inflation

In this paper we show that it is possible to achieve successful hilltop inflation in which the inflaton is identified as the modulus field in a modular invariant theory.The dilaton plays a crucial role in shaping the potential.Modular invariant gaugino condensation provides the mechanism for the modulus stabilisation after inflation. The inflationary trajectory lies on the lower boundary of the fundamental domain of the modulus field τ. Inflation starts near the fixed point τ = i, and ends at a point near τ = ω, which is the global de Sitter vacuum.We investigate the allowed parameter space for successful modular invariant hilltop inflation.

Large curvature fluctuations from no-scale supergravity with a spectator field

We investigate the large curvature perturbations which can lead to the formation of primordial black holes (PBHs) in the context of no-scale supergravity. Our study does not depend on any exotic scenario, such as scalar potentials with inflection points or bulks, and aims to avoid the fine-tuning of model parameters to achieve the formation of PBHs. This formation relies on the quantum fluctuations of a light spectator stochastic field after the inflationary period. Our analysis is based on the SU(2,1)/SU(2)×U(1) symmetry, considering both the inflaton and the spectator field. Specifically, we examine existing no-scale models with Starobinsky-like scalar potentials that are consistent with observable constraints on inflation from measurements of the cosmic microwave background (CMB). These models involve two chiral fields: the inflaton and the modulus field. We propose a novel role for the modulus field as a spectator field, responsible for generating PBHs. Our hypothesis suggests that while the inflaton field satisfies the CMB constraints of inflation, it is the modulus field acting as the spectator that leads to large curvature perturbations, capable to explain the production of PBHs. Additionally, we prioritize retaining the inflationary constraints from the CMB through the consideration of spectator fluctuations. Therefore, by exploring the relationship between these fields within the framework of the SU(2,1)/SU(2)×U(1) symmetry, our aim is to unveil their implications for the formation of PBHs.

Image driven deep learning method with FFT solver for predicting the microscale full field stress of stochastic boundary composites

AbstractA novel image‐driven deep learning approach embedded with model‐data‐knowledge information can directly predict the full field stress distribution and mechanical properties of composites solely based on initial scanning geometry images. The fiber spatial distribution and morphological features are identified by Scanning Electron Microscopy (SEM) initially. An effective random fiber generation algorithm is further utilized to generate images database comprising equivalent geometric models of various microstructures. Subsequently, the geometry model images database is analyzed by fast Fourier transform (FFT) to produce the database including the elastic modulus parameters and full field stress distributions of composites with distinct microstructures. Finally, an innovative image‐learning comprehensive paradigm uniting convolutional neural networks and convolutional autoencoders is elaborated systematically to learn the inherent laws of geometry images and field images. The results show that the proposed method have capacity to effectively and accurately predict the elastic modulus and full field stress distributions combined with error analysis even for stochastic boundary composites. The proposed methodology is a symbiosis of cutting‐edge image learning and non‐destructive testing techniques for composites, which can directly use the local non‐destructive or scanning images of composite structural components to quickly obtain field information and further predict damage evolution online.Highlights Proposing a novel deep learning approach combined with FFT directly to predict stress distribution of stochastic boundary composites solely based on micro‐images. Adopting equivalent geometric models dispersed by higher pixels mesh density considering extreme thin interface. Incorporate adaptive algorithms for streamlined training optimization. An innovative integration of deep learning and non‐destructive testing technology for the stress distribution and properties prediction online.

Finite modular axion and radiative moduli stabilization

We propose a simple setup which can stabilize a modulus field of the finite modular symmetry by the Coleman-Weinberg potential. Our scenario leads to a large hierarchy suppressing instanton-like corrections e2πiτ and to a light axion identified as Reτ, where τ is the modulus field. This stabilization mechanism provides the axion solution to the strong CP problem. The potential has a minimum at a large Imτ which suppresses explicit U(1)PQ violation terms proportional to e−2πImτ, and hence the quality of the axion is ensured by the residual symmetry associated with the T-transformation, τ → τ + 1, around the fixed point τ ∼ i∞.

Tunneling potentials to nothing

The catastrophic decay of a spacetime with compact dimensions, via bubbles of nothing (BoNs), is probably a generic phenomenon. BoNs admit a four-dimensional description as singular Coleman–de Luccia bounces of the size modulus field, stabilized by some potential V(ϕ). We apply the tunneling potential approach to this 4D description to provide a very simple picture of BoNs. Using it, we identify four different types of BoN, corresponding to different classes of higher-dimensional theories. We also identify 4D theories featuring a new type of quenching of BoN decay, which may be present even for dS vacua, and discuss the viability of embedding such models in a higher-dimensional theory. The present approach allows us to treat in a single framework BoN nucleation and other decay channels, and we study the interplay between the different nonperturbative instabilities comparing their decay rates. Published by the American Physical Society 2024

The field of moduli of sets of points in P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^{2}$$\\end{document}

For every n≥6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge 6$$\\end{document}, we give an example of a finite subset of P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^{2}$$\\end{document} of degree n which does not descend to any Brauer–Severi surface over the field of moduli. Conversely, for every n≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\le 5$$\\end{document}, we prove that a finite subset of degree n always descends to a 0-cycle on P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^{2}$$\\end{document} over the field of moduli.

Fields of moduli and the arithmetic of tame quotient singularities

Given a perfect field $k$ with algebraic closure $\overline {k}$ and a variety $X$ over $\overline {k}$, the field of moduli of $X$ is the subfield of $\overline {k}$ of elements fixed by field automorphisms $\gamma \in \operatorname {Gal}(\overline {k}/k)$ such that the Galois conjugate $X_{\gamma }$ is isomorphic to $X$. The field of moduli is contained in all subextensions $k\subset k'\subset \overline {k}$ such that $X$ descends to $k'$. In this paper, we extend the formalism and define the field of moduli when $k$ is not perfect. Furthermore, Dèbes and Emsalem identified a condition that ensures that a smooth curve is defined over its field of moduli, and prove that a smooth curve with a marked point is always defined over its field of moduli. Our main theorem is a generalization of these results that applies to higher-dimensional varieties, and to varieties with additional structures. In order to apply this, we study the problem of when a rational point of a variety with quotient singularities lifts to a resolution. As a consequence, we prove that a variety $X$ of dimension $d$ with a smooth marked point $p$ such that $\operatorname {Aut}(X,p)$ is finite, étale and of degree prime to $d!$ is defined over its field of moduli.

Resolving engineering challenges: Deep learning in frequency domain for 3D inverse identification of heterogeneous composite properties

The inverse identification of heterogeneous composite properties from measured displacement/strain fields is pivotal in engineering. Traditional methodologies and emerging machine learning techniques both confront two major challenges. The first challenge involves achieving rapid identification while maintaining robustness to noise or pollution, and the second pertains to applicability in resolving complex three-dimensional (3D) engineering problems. To address these issues, a novel deep learning in frequency domain method (DLfd) for 3D inverse identification is proposed. Utilizing 3D-discrete cosine transform (3D-DCT), this method reduces input dimension by 98.24%, thereby simplifying the 3D problem to a computationally manageable form. A subsequent U-Net model establishes high-precision mappings between the reduced 3D-DCT coefficients of strain fields and modulus field, and the L1-error for the predicted modulus field is remarkably low at 2.431%. Even facing large noise (5% level) interference, the L1-error increases only 0.1%, demonstrating the robustness of the method. Coupled with Bayesian optimization, DLfd can generate accurate predictions even with incomplete measurements, and has been validated through several case studies involving measured fields missing in various shapes and locations. The method demonstrates general applicability to both 2D and 3D scenarios, and effectively mitigates the challenges posed by noise and data pollution, bringing it a step closer to practical implementation.

Bubbles of nothing:the tunneling potential approach

Bubbles of nothing (BoNs) describe the decay of spacetimes with compact dimensions and are thus of fundamental importance for many higher dimensional theories proposed beyond the Standard Model. BoNs admit a 4-dimensional description in terms of a singular Coleman-de Luccia (CdL) instanton involving the size modulus field, stabilized by some potential V(ϕ). Using the so-called tunneling potential (Vt ) approach, we study which types of BoNs are possible and for which potentials V(ϕ) can they be present. We identify four different types of BoN, characterized by different asymptotic behaviours at the BoN core and corresponding to different classes of higher dimensional theories, which we also classify. Combining numerous analytical and numerical examples, we study the interplay of BoN decays with other standard decay channels, identify the possible types of quenching of BoN decays and show how BoNs for flux compactifications can also be described in 4 dimensions by a multifield Vt . The use of the Vt approach greatly aids our analyses and offers a very simple picture of BoNs which are treated in the same language as any other standard vacuum decays.

Revisiting Trimaximal TM2 mixing in two A4 modular symmetries

In this paper, we discuss a minimal lepton flavor model with two modular [Formula: see text] symmetries, one acting on neutrinos and the other acting on charged leptons. Two corresponding moduli fields are restricted at stabilizers. To avoid vanishing or degenerate lepton masses, the stabilizer in the charged lepton sector always preserves a [Formula: see text] symmetry, and that in the neutrino preserves a [Formula: see text] symmetry. By scanning all viable stabilizers, a unique Trimaximal TM2 mixing is predicted. However, the prediction of the lightest neutrino mass and the mass parameter in neutrinoless double beta decay, as well as two Majorana phases, are different and classified into three cases.

The field of moduli of varieties with a structure

If X is a variety with an additional structure ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}, such as a marked point, a divisor, a polarization, a group structure and so forth, then it is possible to study whether the pair (X,ξ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(X,\\xi )$$\\end{document} is defined over the field of moduli. There exists a precise definition of “algebraic structures” which covers essentially all of the obvious concrete examples. We prove several formal results about algebraic structures. There are immediate applications to the study of fields of moduli of curves and finite sets in P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}^{2}$$\\end{document}, but the results are completely general. Fix G a finite group of automorphisms of X, a G-structure is an algebraic structure with automorphism group equal to G. First, we prove that G-structures on X are in a 1 : 1 correspondence with twisted forms of X/G⤏BG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X/G\\dashrightarrow \\mathscr {B}G$$\\end{document}. Secondly we show that, under some assumptions, every algebraic structure on X is equivalent to the structure given by some 0-cycle. Third, we give a cohomological criterion for checking the existence of G-structures not defined over the field of moduli. Fourth, we identify geometric conditions about the action of G on X which ensure that every G-structure is defined over the field of moduli.

The emergence proposal and the emergent string

We explore the Emergence Proposal for the moduli metric and the gauge couplings in a concrete model with 7 saxionic and 7 axionic moduli fields, namely the compactification of the type IIA superstring on a 6-dimensional toroidal orbifold. We show that consistency requires integrating out precisely the 12 towers of light particle species arising from KK and string/brane winding modes and one asymptotically tensionless string up to the species scale. After pointing out an issue with the correct definition of the species scale in the presence of string towers, we carry out the emergence computation and find that the KK and winding modes indeed impose the classical moduli dependence on the one-loop corrections, while the emergent string induces moduli dependent logarithmic suppressions. The interpretation of these results for the Emergence Proposal are discussed revealing a couple of new and still not completely settled aspects.

Characteristic analysis of a novel magnetorheological fabric composite cored flexible sandwich beam with tunable stiffness

This paper focuses on the performance improvement and evaluation of a novel flexible sandwich beam incorporated magnetorheological fluid porous fabric (MRF-PF). As a novel MR material, MRF-PF has been introduced, prepared, and measured to analyze the pre-yield property between complex shear modulus and magnetic fields. MRF-PF is used into the flexible sandwich beam as core layer. Pre-yield property with tunable stiffness is used to adjust the dynamic response. Then, a theoretical model is derived which can precisely describe the performance. Based on experimental results, sandwich beam incorporated MRF-PF has a good performance of controllability. When the magnetic field is applied into the free end, the natural frequency decreases with increasing the currents and filling ratio. In contrast, the frequency and amplitude increase when the clamped end is exposed to the magnetic fields. Comparing with other investigations, this proposed sandwich beam incorporated MRF-PF has a larger frequency range. The first and second natural frequency show the increases of 54.8% and 77.2%, respectively. The reduction of amplitude is closely related to the thickness of face plate. Therefore, the performance of the compound sandwich beam can be significantly improved by MRF-PF.

Regular dessins with moduli fields of the form Q(ζp, \sqrt[p]{q})

Gareth Jones asked during the 2014 SIGMAP conference for examples of regular dessins with nonabelian fields of moduli. In this paper, we first construct dessins whose moduli fields are nonabelian Galois extensions of the form Q(ζp, \sqrt[p]{q}), where p is an odd prime and ζp is a pth root of unity and q ∈ Q is not a pth power, and we then show that their regular closures have the same moduli fields. Finally, in the special case p = q = 3 we give another example of a regular dessin with moduli field Q(ζ3, ∛(3)) of degree 219 · 34 and genus 14155777.

Displacement-based structural identification using differentiable physics

Infrastructure is at constant risk of failure due to internal or hidden damage resulting from environmental conditions, variability in building materials, and fabrication errors. These risks can be mitigated by structural health monitoring, but it is difficult to monitor the state of the entire structure using discrete measurements. In this study, we propose a scheme for estimating spatially varying elastic modulus fields of a structural element using differentiable physics to support structural health monitoring efforts. Our approach is evaluated on two numerical model systems, a cantilever beam and a simply supported beam, and systematically evaluated for its sensitivity to initialization, boundary conditions, and a wide variety of spatially varying modulus fields. The results demonstrate the effectiveness of this approach in finding structures with matching displacement responses, while also highlighting its limitations in recovering accurate material properties, as is common in with all inverse methods. To address these limitations, we employ regularization techniques including blur filters and Heaviside projection to mitigate degeneracy and recover more complex fields. This work lays the foundation for more informed decision-making in structural health monitoring, with especially close applications to digital image correlation based approaches.

On string one-loop correction to the Einstein-Hilbert term and its implications on the Kähler potential

To compute the string one-loop correction to the Kähler potential of moduli fields of string compactifications in Einstein-frame, one must compute: the string one-loop correction to the Einstein-Hilbert action, the string one-loop correction to the moduli kinetic terms, the string one-loop correction to the definition of the holomorphic coordinates. In this note, in the small warping limit, we compute the string one-loop correction to the Einstein-Hilbert action of type II string theory compactified on orientifolds of Calabi-Yau threefolds. We find that the one-loop correction is determined by the new supersymmetric index studied by Cecotti, Fendley, Intriligator, and Vafa and the Witten index. As a simple application, we apply our results to estimate the size of the one-loop corrections around a conifold point in the Kähler moduli space.