Moduli Problem Research Articles

Low-scale supersymmetry from inflation

We investigate an inflation model with the inflaton being identified with a Higgs boson responsible for the breaking of U(1)B−L symmetry. We show that supersymmetry must remain a good symmetry at scales one order of magnitude below the inflation scale, in order for the inflation model to solve the horizon and flatness problems, as well as to account for the observed density perturbation. The upper bound on the soft supersymmetry breaking mass lies between 1 TeV and 103 TeV. Interestingly, our finding opens up a possibility that universes with the low-scale supersymmetry are realized by the inflationary selection. Our inflation model has rich implications; non-thermal leptogenesis naturally works, and the gravitino and moduli problems as well as the moduli destabilization problem can be solved or ameliorated; the standard-model higgs boson receives a sizable radiative correction if the supersymmertry breaking takes a value on the high side ∼ 103 TeV.

On a theorem of Castelnuovo and applications to moduli

In this paper we prove a theorem stated by Castelnuovo which bounds the dimension of linear systems of plane curves in terms of two invariants, one of which is the genus of the curves in the system. Then we classify linear systems whose dimension belongs to certain intervals which naturally arise from Castelnuovo's theorem. Finally we make an application to the following moduli problem: what is the maximum number of moduli of curves of geometric genus $g$ varying in a linear system on a surface? It turns out that, for $g\ge 22$, the answer is $2g+1$, and it is attained by trigonal canonical curves varying on a balanced rational normal scroll.

Smoothable del Pezzo surfaces with quotient singularities

AbstractWe classify del Pezzo surfaces with quotient singularities and Picard rank one which admit a ℚ-Gorenstein smoothing. These surfaces arise as singular fibres of del Pezzo fibrations in the 3-fold minimal model program and also in moduli problems.

Neutrino masses, Baryon asymmetry, dark matter and the moduli problem — A complete framework

Recent developments in string theory have led to ``realistic string compactifications which lead to moduli stabilization while generating a hierarchy between the Electroweak and Planck scales at the same time. However, this seems to suggest a rethink of our standard notions of cosmological evolution after the end of inflation and before the beginning of BBN. This epoch is crucial for addressing the issues of neutrino masses, baryon asymmetry, Dark Matter (DM) abundance and the moduli (gravitino) problem. We argue that within classes of realistic string compactifications as defined above, there generically exists a light modulus with a mass comparable to that of the gravitino which is typically much smaller than the Hubble parameter during inflation. Therefore, it is destabilized and generates a large late-time entropy when it decays. Thus, all known elegant mechanisms of generating the baryon asymmetry of the Universe in the literature have to take this fact into account. In this work, we find that it is still possible to naturally generate the observed baryon asymmetry of the Universe as well as light left-handed neutrino masses from a period of Affleck-Dine (AD) leptogenesis shortly after the end of inflation, in classes of realistic string constructions with a minimal extension of the MSSM below the unification scale (consisting only of right-handed neutrinos) and satisfying certain microscopic criteria described in the text. The AD mechanism has already been used to generate the baryon asymmetry in the literature; however in this work we have embedded the above mechanism within a framework well motivated from string theory and have tried to describe the epoch from the end of inflation to the beginning of BBN in a complete and self-consistent manner. The consequences of our analysis are as follows. The lightest left-handed neutrino is required to be virtually massless. The moduli (gravitino) problem can be naturally solved in this framework both within gravity and gauge mediation. The observed upper bound on the relic abundance constrains the moduli-matter and moduli-gravitino couplings since the DM is produced non-thermally within this framework. Finally, although not a definite prediction, the framework naturally allows a light right-handed neutrino and sneutrinos around the electroweak scale which could have important implications for the nature of DM as well as the LHC.

Cosmological moduli problem from thermal effects

We estimate the cosmological abundance of a modulus field that has dilatonic couplings to gauge fields, paying particular attention to thermal corrections on the modulus potential. We find that a certain amount of the modulus coherent oscillations is necessarily induced by a linear thermal effect. We argue that such an estimate provides the smallest possible modulus abundance for a given thermal history of the Universe. As an example we apply our results to a saxion, a bosonic supersymmetric partner of an axion, and derive a tight bound on the reheating temperature. We emphasize that the problem cannot be avoided by fine-tuning the initial deviation of the modulus field, since the minimal amount of the modulus is induced by the dynamics of the scalar potential.

Non-thermal dark matter and the moduli problem in string frameworks

We address the cosmological moduli/gravitino problems and the issue of too little thermal but excessive non-thermal dark matter from the decays of moduli. The main examples we study are the G2-MSSM models arising from M theory compactifications, which allow for a precise calculation of moduli decay rates and widths. We find that the late decaying moduli satisfy both BBN constraints and avoid the gravitino problem. The non-thermal production of Wino LSPs, which is a prediction of G2-MSSM models, gives a relic density of about the right order of magnitude.

Moduli problem and points on some twisted Shimura varieties of PEL type

In this article we describe the moduli problem of a “twist” of some simple Shimura varieties of PEL type that appear in Kottwitz's papers [R. Kottwitz, Shimura varieties and λ-adic representations, in: Automorphic Forms, Shimura Varieties and L-Functions, part 1, in: Perspect. Math., vol. 10, Academic Press, San Diego, CA, 1990, pp. 161–209; R. Kottwitz, Points on some Shimura varieties over finite fields, J. Amer. Math. Soc. 5 (2) (1992) 373–444] and [R. Kottwitz, On the λ-adic representations associated to some simple Shimura varieties, Invent. Math. 108 (1992) 653–665] and then, using the moduli problem, we compute the cardinality of the set of points over finite fields of the twisted Shimura varieties. Using this result, we compute the zeta function of the twisted varieties. The twist of the Shimura varieties is done by a mod q representation of the absolute Galois group of the reflex field of the Shimura varieties.

Applying the equivalent section method to solve beam subjected to lateral force and bending-compression column with different moduli

Based on elastic theory of different tension-compression moduli, bending beam subjected to lateral force and bending-compression column with different moduli were solved by the equivalent section method. Formulas for the neutral axis, normal stress, shear stress and displacement were developed also. This equivalent section method can turn conveniently different moduli problems into the similar moduli ones, i.e., classical elasticity problems so the existent results aimed beams and columns with similar moduli both can be used indiscriminately without complicated derived process. Compared with the present derived method based on different moduli theory the applicability and efficiency of equivalent section method is demonstrated.

Gravitino production from heavy moduli decay and cosmological moduli problem revived

The cosmological moduli problem for relatively heavy moduli fields is reinvestigated. For this purpose we examine the decay of a modulus field at a quantitative level. The modulus dominantly decays into gauge bosons and gauginos, provided that the couplings among them are not suppressed in the gauge kinetic function. Remarkably the modulus decay into a gravitino pair is unsuppressed generically, with a typical branching ratio of order 0.01. Such a large gravitino yield after the modulus decay causes cosmological difficulties. The constraint from the big-bang nucleosynthesis pushes up the gravitino mass above 10^5 GeV. Furthermore to avoid the over-abundance of the stable neutralino lightest superparticles (LSPs), the gravitino must weigh more than about 10^6 GeV for the wino-like LSP, and even more for other neutralino LSPs. This poses a stringent constraint on model building of low-energy supersymmetry.

Truncated resolution model structures

Using the dual of Bousfield–Friedlander localization, we colocalize resolution model structures on cosimplicial objects over a left proper model category to get truncated resolution model structures. These are useful for studying realization and moduli problems in algebraic topology.

JACOBI COHOMOLOGY, LOCAL GEOMETRY OF MODULI SPACES, AND HITCHIN CONNECTIONS

We develop some cohomological tools for the study of the local geometry of moduli and parameter spaces in complex Algebraic Geometry. Notably, we develop canonical formulae for the differential operators of arbitrary order and their natural action on suitable `natural' modules (for example, functions); in particular, we obtain a formula, in terms of the moduli problem, for the Lie bracket of vector fields on a moduli space. As an application, we obtain another construction and proof of flatness for the familiar KZW or Hitchin connection on moduli spaces of curves.

Kachru-Kallosh-Linde-Trivedi-type models with moduli-mixing superpotential

We study KKLT type models with moduli-mixing superpotential. In several string models, gauge kinetic functions are written as linear combinations of two or more moduli fields. Their gluino condensation generates moduli-mixing superpotential. We assume one of moduli fields is frozen already around the string scale. It is found that K\"ahler modulus can be stabilized at a realistic value without tuning 3-form fluxes because of gluino condensation on (non-)magnetized D-brane. Furthermore, we do not need to highly tune parameters in order to realize a weak gauge coupling and a large hierarchy between the gravitino mass and the Planck scale, when there exists non-perturbative effects on D3-brane. SUSY breaking patterns in our models have a rich structure. Also, some of our models have cosmologically important implications, e.g., on the overshooting problem and the destabilization problem due to finite temperature effects as well as the gravitino problem and the moduli problem.

Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC

The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work, which may also address the hierarchy problem. An example -- supported by Weinberg's successful prediction of the cosmological constant -- is the potentially vast landscape of vacua in string theory, where the existence of galaxies and atoms is promoted to a vacuum selection criterion. Then, low energy SUSY becomes unnecessary, and supersymmetry -- if present in the fundamental theory -- can be broken near the unification scale. All the scalars of the supersymmetric standard model become ultraheavy, except for a single finely tuned Higgs. Yet, the fermions of the supersymmetric standard model can remain light, protected by chiral symmetry, and account for the successful unification of gauge couplings. This framework removes all the difficulties of the SSM: the absence of a light Higgs and sparticles, dimension five proton decay, SUSY flavor and CP problems, and the cosmological gravitino and moduli problems. High-scale SUSY breaking raises the mass of the light Higgs to about 120-150 GeV. The gluino is strikingly long lived, and a measurement of its lifetime can determine the ultraheavy scalar mass scale. Measuring the four Yukawa couplings of the Higgs to the gauginos and higgsinos precisely tests for high-scale SUSY. These ideas, if confirmed, will demonstrate that supersymmetry is present but irrelevant for the hierarchy problem -- just as it has been irrelevant for the cosmological constant problem -- strongly suggesting the existence of a fine-tuning mechanism in nature.

Hybrid inflation and the moduli problem

We revisit some questions in supersymmetric hybrid inflation. We analyze the amount of fine-tuning required in various models, the problem of decay at the end of inflation and the generation of baryons after inflation. We find that the most natural setting for hybrid inflation is in supersymmetric models with nonrenormalizable couplings. Furthermore, we argue that almost inevitably, one of the fields involved is a modulus, with Planck scale variation. The resulting moduli problem can be solved in two ways: either by a massive modulus (which requires some fine-tuning), or an enhanced symmetry point, in which the moduli becomes strongly coupled to the standard model. Various possibilities for baryon production are discussed.

The realization space of a $Pi;-algebra: a moduli problem in algebraic topology

A Π -algebra A is a graded group with all of the algebraic structure possessed by the homotopy groups of a pointed connected topological space. We study the moduli space R ( A ) of realizations of A , which is defined to be the disjoint union, indexed by weak equivalence classes of CW-complexes X with π ∗ (X)=A , of the classifying space of the monoid of self homotopy equivalences of X . Our approach amounts to a kind of homotopical deformation theory: we obtain a tower whose homotopy limit is R ( A ), in which the space at the bottom is BAut ( A ) and the successive fibres are determined by Π -algebra cohomology. (This cohomology is the analog for Π -algebras of the Hochschild cohomology of an associative ring or the André-Quillen cohomology of a commutative ring.) It seems clear that the deformation theory can be applied with little change to study other moduli problems in algebra and topology.

The realization space of a Π-algebra: a moduli problem in algebraic topology

A Π-algebra A is a graded group with all of the algebraic structure possessed by the homotopy groups of a pointed connected topological space. We study the moduli space R( A) of realizations of A, which is defined to be the disjoint union, indexed by weak equivalence classes of CW-complexes X with π ∗(X)=A , of the classifying space of the monoid of self homotopy equivalences of X. Our approach amounts to a kind of homotopical deformation theory: we obtain a tower whose homotopy limit is R( A), in which the space at the bottom is BAut( A) and the successive fibres are determined by Π-algebra cohomology. (This cohomology is the analog for Π-algebras of the Hochschild cohomology of an associative ring or the André-Quillen cohomology of a commutative ring.) It seems clear that the deformation theory can be applied with little change to study other moduli problems in algebra and topology.

Noncommutative algebraic geometry

The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure. In this paper we shall show that one may overcome these difficulties by introducing a noncommutative algebraic geometry, where affine “schemes” are modeled on associative algebras. The points of such an affine scheme are the simple modules of the algebra, and the local structure of the scheme at a finite family of points, is expressed in terms of a noncommutative deformation theory proposed by the author in [10]. More generally, the geometry in the theory is represented by a swarm , i.e. a diagram (finite or infinite) of objects (and if one wants, arrows) in a given k -linear Abelian category ( k a field), satisfying some reasonable conditions. The noncommutative deformation theory refered to above, permits the construction of a presheaf of associative k -algebras, locally parametrizing the diagram. It is shown that this theory, in a natural way, generalizes the classical scheme theory. Moreover it provides a promising framework for treating problems of invariant theory and moduli problems. In particular it is shown that many moduli spaces in classical algebraic geometry are commutativizations of noncommutative schemes containing additional information.

Relativistic Stars in Randall-Sundrum Gravity

We review the non-linear behavior of compactifications with localized brane matter discussed in [1]. The example chosen to test is Randall-Sundrum gravity, with one brane, having no moduli problem and reproducing astrophysical gravity in the long wavelength linear regime. The full 5-dimensional Einstein equations are solved numerically for static spherically symmetric matter localized on the brane, yielding regular geometries in the bulk with axial symmetry. The algorithm performs best for small stars (radius less than the AdS length) yielding highly non-linear solutions, photons emitted from the stellar core having redshifts up to [Formula: see text]. An upper mass limit is observed in these small stars. We are able to show that the intrinsic geometry of large stars, with radius several times the AdS length, is described by 4-dimensional General Relativity past the perturbative regime and up to the largest mass stars studied with core photon redsbifts of [Formula: see text].

Moduli problems of sheaves associated with oriented trees

To every oriented tree we associate vector bundle problems. We define semistability concepts for these vector bundle problems and establish the existence of moduli spaces. As an important application, we obtain an algebraic construction of the moduli space of holomorphic triples.

RADION POTENTIAL AND BRANE DYNAMICS

We examine the cosmology of Randall–Sundrum model in a dynamic setting where scalar fields are present in the bulk as well as the branes. This generates a mechanism similar to that of Goldberger–Wise for radion stabilization and the recovery of late-time cosmology features on the branes. Due to the induced radion dynamics, the inflating branes roll towards the minimum of the radion potential, thereby exiting inflation and reheating the universe. In the slow roll part of the potential, the TeV branes have maximum inflation rate and energy as their coupling to the radion and bulk modes have minimum suppression. Hence, when rolling down the steep end of the potential towards the stable point, the radion field (which appears as the inflaton of the effective 4-D theory in the branes) decays very fast and reheats the universe. This process results in a decrease of the brane's canonical vacuum energy, Λ4. However, at the minimum of the potential Λ4 is small but not necessarily zero and the fine-tuning issue remains. Density perturbation constraints introduce an upper bound on Λ4. Due to the large radion mass and strong suppression to the bulk modes, moduli problems and bulk reheating do not occur. The reheat temperature and a sufficient number of e-folding constraints for the brane-universe are also satisfied. The model therefore recovers the radiation dominated FRW universe.