Moduli Fields Research Articles

Direct error in constitutive equation formulation for plane stress inverse elasticity problem

We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation with a momentum equation constraint. Numerical results on model problems show that the formulation is capable of handling discontinuous and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown.

Chow group of 0-cycles with modulus and higher-dimensional class field theory

One of the main results of this paper is a proof of the rank one case of an existence conjecture on lisse l-adic sheaves on a smooth variety over a finite field due to Deligne and Drinfeld. The problem is translated into the language of higher dimensional class field theory over finite fields, which describes the abelian fundamental group by Chow groups of zero cycles with moduli. A key ingredient is the construction of a cycle theoretic avatar of refined Artin conductor in ramification theory originally studied by Kazuya Kato.

An elastoplastic bounding surface model for the cyclic undrained behaviour of saturated soft clays

A total stress-based bounding surface model is developed to predict the undrained behaviour of saturated soft clays under cyclic loads based on the anisotropic hardening modulus field and bounding-surface theories. A new hardening rule is developed based on a new interpolation function of the hardening modulus that has simple mathematic expression and fewer model parameters. The evolution of hardening modulus field is described in the deviatoric stress space. It is assumed that the stress reverse points are the mapping centre points and the mapping centre moves with the variation of loading and unloading paths to describe the cyclic stress-strain hysteresis curve. In addition, by introducing a model parameter that reflects the accumulation rate and level of shear strain to the interpolation function, the cyclic shakedown and failure behaviour of soil elements with different combinations of initial and cyclic stresses can be captured. The methods to determine the model parameters using cyclic triaxial compression tests are also studied. Finally, the cyclic triaxial extension and torsional shear tests are performed. By comparing the predictions with the test results, the model can be used to describe undrained cyclic stress-strain responses of elements with different stress states for the tested clays.

Electroweak vacuum stabilized by moduli during/after inflation

It is known that the present electroweak vacuum is likely to be metastable and it may lead to a serious instability during/after inflation. We propose a simple solution to the problem of vacuum instability during/after inflation. If there is a moduli field which has Planck-suppressed interactions with the standard model fields, the Higgs quartic coupling in the early universe naturally takes a different value from the present one. A slight change of the quartic coupling in the early universe makes the Higgs potential absolutely stable and hence we are free from the vacuum instability during/after inflation.

Modular invariant inflation

Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field T whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by T. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential Vht, but it also has a non-negligible deviation from Vht. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.

Dilaton stabilization in three-generation heterotic string model

We study dilaton stabilization in heterotic string models. By utilizing the asymmetric orbifold construction, we construct an explicit three-generation model whose matter content in the visible sector is the supersymmetric standard model with additional vectorlike matter. This model does not contain any geometric moduli fields except the dilaton field. Model building at a symmetry enhancement point in moduli space enlarges the rank of the hidden gauge group. By analyzing multiple hidden gauge sectors, the dilaton field is stabilized by the racetrack mechanism. We also discuss a supersymmetry breaking scenario and F-term uplifting.

A TOWER OF RIEMANN SURFACES WHICH CANNOT BE DEFINED OVER THEIR FIELD OF MODULI

AbstractExplicit examples of both hyperelliptic and non-hyperelliptic curves which cannot be defined over their field of moduli are known in the literature. In this paper, we construct a tower of explicit examples of such kind of curves. In that tower there are both hyperelliptic curves and non-hyperelliptic curves.

Explicitly broken supersymmetry with exactly massless moduli

There is an avatar of the little hierarchy problem of the MSSM in 3-dimensional supersymmetry. We propose a solution to this problem in AdS$_3$ based on the AdS/CFT correspondence. The bulk theory is a supergravity theory in which U(1) $\times$ U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. Since the R-charges of scalar and spinor differ, this generates a SUSY breaking shift of their masses. The Ward identity facilitates the calculation of these mass shifts to any desired order in the strength of the deformation. Moduli fields are massless $R$-neutral bulk scalars with vanishing potential in the undeformed theory. These properties are maintained to all orders in the deformation despite the fact that moduli couple in the bulk to loops of R-charged fields.

Moduli mediation without moduli-induced gravitino problem

We study the moduli-induced gravitino problem within the framework of the phenomenologically attractive mirage mediations. The huge amount of gravitino generated by the moduli decay can be successfully diluted by introducing an extra light modulus field which does not induce the supersymmetry breaking. Since the lifetime of extra modulus field becomes longer than usually considered modulus field, our proposed mechanism is applied to both the low- and high-scale supersymmetry breaking scenarios. We also point out that such an extra modulus field appears in the flux compactification of type II string theory.

An explicit quasiplatonic curve with non-abelian moduli field

We give an example of a regular dessin d'enfant whose field of moduli is not an abelian extension of the rational numbers, namely it is the field generated by a cubic root of 2. This answers a previous question. We also prove that the underlying curve has non-abelian field of moduli itself, giving an explicit example of a quasiplatonic curve with non-abelian field of moduli. In the last section, we note that two examples in previous literature can be used to find other examples of regular dessins d'enfants with non-abelian field of moduli.

The axiverse induced dark radiation problem

The string/$M$ theory Axiverse -- a plethora of very light Axion Like Particles (ALPs) with a vast range of masses -- is arguably a generic prediction of string/$M$ theory. String/$M$ theory also tends to predict that the early Universe is dominated by moduli fields. When the heavy moduli decay, before nucleosynthesis, they produce dark radiation in the form of relativistic ALPs. Generically one estimates that the number of relativistic species grows with the number of axions in the Axiverse, in contradiction to the observations that $N_{eff} \leq 4$. We explain this problem in detail and suggest some possible solutions to it. The simplest solution requires that the lightest modulus decays only into its own axion superpartner plus Standard Model particles and this severely constrains the moduli Kahler potential and mass matrix.

Can thermal inflation be consistent with baryogenesis in gauge-mediated SUSY breaking models?

Thermal inflation is an attractive idea to dilute cosmic density of unwanted particles such as moduli fields which cause cosmological difficulties. However, it also dilutes preexisting baryon asymmetry and some viable baryogenesis is necessary for a cosmologically consistent scenario. We investigate whether the Affleck-Dine mechanism can produce baryon asymmetry enough to survive after the dilution in gauge-mediated SUSY breaking models. Flat directions except for $LH_u$ flat direction cannot provide such huge baryon number because of Q-ball formation. We show that although the $LH_u$ flat direction is special in terms of having $\mu$-term which prevents Q-ball formation, it cannot explain the observed baryon asymmetry either.

Dark matter production mechanisms with a nonthermal cosmological history: A classification

We perform a comprehensive study of models of dark matter (DM) in a Universe with a non-thermal cosmological history, i.e with a phase of pressure-less matter domination before the onset of big-bang nucleosynethesis (BBN). Such cosmological histories are generically predicted by UV completions that contain gravitationally coupled scalar fields (moduli). We classify the different production mechanisms for DM in this framework, generalizing previous works by considering a wide range of DM masses/couplings and allowing for DM to be in equilibrium with a "dark" sector. We identify four distinct parametric regimes for the production of relic DM, and derive accurate semi-analytic approximations for the DM relic abundance. Our results are particularly relevant for supersymmetric theories, in which the standard non-thermally produced DM candidates are disfavored by indirect detection constraints. We also comment on experimental signals in this framework, focusing on novel effects involving the power spectrum of DM density perturbations. In particular, we identify a class of models where the spectrum of DM density perturbations is sensitive to the pressure-less matter dominated era before BBN, giving rise to interesting astrophysical signatures to be looked for in the future. A worthwhile future direction would be to study well-motivated theoretical models within this framework and carry out detailed studies of the pattern of expected experimental signals.

Nonperturbative overproduction of axionlike particles via derivative interactions

Axion like particles (ALPs) are quite generic in many scenarios for physics beyond the Standard Model, they are pseudoscalar Nambu-Goldstone bosons, and appear once any global $U(1)$ symmetry is broken spontaneously. The ALPs can gain mass from various non-perturbative quantum effects, such as anomalies or instantons. ALPs can couple to the matter sector incluidng a scalar condensate such as inflaton or moduli field via derivative interactions, which are suppressed by the axion {\it decay constant}, $f_\chi$ . Although weakly interacting, the ALPs can be produced abundantly from the coherent oscillations of a homogeneous condensate. In this paper we will study such a scenario where the ALPs can be produced abundantly, and in some cases can even overclose the Universe via odd and even dimensional operators, as long as $f_\chi/\Phi_{\rm I} \ll 1$, where $\Phi_{\rm I}$ denotes the initial amplitude of the coherent oscillations of the scalar condensate, $\phi$. We will briefly mention how such dangerous overproduction would affect dark matter and dark radiation abundances in the Universe.

The D-material universe

In a previous publication by some of the authors (N.E.M., M.S. and M.F.Y.), we have argued that the ``D-material universe'', that is a model of a brane world propagating in a higher-dimensional bulk populated by collections of D-particle stringy defects, provides a model for the growth of large-scale structure in the universe via the vector field in its spectrum. The latter corresponds to D-particle recoil velocity excitations as a result of the interactions of the defects with stringy matter and radiation on the brane world. In this article, we first elaborate further on the results of the previous study on the galactic growth era and analyse the circumstances under which the D-particle recoil velocity fluid may ``mimic'' dark matter in galaxies. A lensing phenomenology is also presented for some samples of galaxies, which previously were known to provide tension for modified gravity (TeVeS) models. The current model is found in agreement with these lensing data. Then we discuss a cosmic evolution for the D-material universe by analysing the conditions under which the late eras of this universe associated with large-scale structure are connected to early epochs, where inflation takes place. It is shown that inflation is induced by dense populations of D-particles in the early universe, with the rôle of the inflaton field played by the condensate of the D-particle recoil-velocity fields under their interaction with relativistic stringy matter, only for sufficiently large brane tensions and low string mass scales compared to the Hubble scale. On the other hand, for large string scales, where the recoil-velocity condensate fields are weak, inflation cannot be driven by the D-particle defects alone. In such cases inflation may be driven by dilaton (or other moduli) fields in the underlying string theory.

Disappearing inflaton potential via heavy field dynamics

We propose a possibility that the inflaton potential is significantly modified after inflation due to heavy field dynamics. During inflation such a heavy scalar field may be stabilized at a value deviated from the low-energy minimum. In extreme cases, the inflaton potential vanishes and the inflaton becomes almost massless at some time after inflation. Such transition of the inflaton potential has interesting implications for primordial density perturbations, reheating, creation of unwanted relics, dark radiation, and experimental search for light degrees of freedom. To be concrete, we consider a chaotic inflation in supergravity where the inflaton mass parameter is promoted to a modulus field, finding that the inflaton becomes stable after the transition and contributes to dark matter. Another example is a hilltop inflation (also called new inflation) by the MSSM Higgs field which acquires a large expectation value just after inflation, but it returns to the origin after the transition and finally rolls down to the electroweak vacuum. Interestingly, the smallness of the electroweak scale compared to the Planck scale is directly related to the flatness of the inflaton potential.

Nonuniversal gaugino masses in a magnetized toroidal compactification of SYM theories

This paper proposes a concrete model of nonuniversal gaugino masses on the basis of higher-dimensional supersymmetric Yang-Mills theories compactified on a magnetized factorizable torus, and we estimate the gauge coupling constants and gaugino masses in the model. In the magnetized toroidal compactifications, the four-dimensional effective action can be obtained analytically identifying its dependence on moduli fields, where the magnetic fluxes are able to yield the flavor structure of the minimal supersymmetric standard model (MSSM). The obtained gauge kinetic functions contains multi moduli fields and their dependence is nonuniversal for the three gauge fields. The nonuniversal gauge kinetic functions can lead to nonuniversal gaugino masses at a certain high energy scale (e.g. compactification scale). Our numerical analysis of them shows that, particular ratios of gaugino masses, which were found to enhance the Higgs boson mass and lead to “natural supersymmetry” in the MSSM, can be realized in our model, while the gauge couplings are unified as is achieved in the MSSM.

Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group

This paper is devoted to the explicit description of the Galois descent obstruction for hyperelliptic curves of arbitrary genus whose reduced automorphism group is cyclic of order coprime to the characteristic of their ground field. Along the way, we obtain an arithmetic criterion for the existence of a hyperelliptic descent. The obstruction is described by the so-called arithmetic dihedral invariants of the curves in question. If it vanishes, then the use of these invariants also allows the explicit determination of a model over the field of moduli; if not, then one obtains a hyperelliptic model over a degree 2 extension of this field.

Picard-Shimura class fields corresponding to a family of hyperelliptic curves

We know explicit Picard modular functions, corresponding to a family of hyperelliptic curves, with the property that their values in CM points generate abelian extensions of the associated reflex fields (Matsumoto, Ann Sc Norm Sup Pisa 16(4):557–578, 1989, Riedel, In: Arithmetic and geometry around hypergeometric functions. Birkhauser, Basel, 2007, pp 273–285). In this note we study the number fields and their extensions occuring in this way. We show that every sextic CM field containing the fourth roots of unity is projectively generated by a singular modulus and appears as reflex field. In order to investigate the abelian extensions, we use the class field theoretic description of the field of moduli. In the unramified case we develop conditions that assure that the Picard-Shimura class field is equal to the reflex field or to the Hilbert class field. Finally, we determine these class fields for odd class numbers up to 11.

Fields of moduli of some special curves

In this paper we provide necessary conditions for a curve to be definable over its field of moduli. These conditions generalize the results known for the hyperelliptic case by B. Huggins and for normal cyclic p-gonal curves by A. Kontogeorgis.