Points Of Enhanced Symmetry Research Articles

Moduli trapping mechanism in modular flavor symmetric models

We discuss how the moduli in modular flavor symmetric models dynamically select enhanced symmetry points at which the residual modular symmetry renders extra matter fields massless. The moduli dynamics non-perturbatively produces the extra matter particles, which gives (time-dependent) effective potential that traps the moduli to enhanced symmetry points. We show analytic estimates of particle production rate consistent with numerical results, and the dynamics of moduli based on the analytic estimates.

Waterfall stiff period can generate observable primordial gravitational waves

A toy-model is studied, which considers two flat directions meeting at an enhanced symmetry point such that they realise the usual hybrid inflation mechanism. The kinetic term of the waterfall field features a pole at its Planckian vacuum expectation value (VEV), as with α-attractors. Consequently, after the phase transition which terminates hybrid inflation, the waterfall field never rolls to its VEV. Instead, it drives a stiff period, where the barotropic parameter of the Universe w ≈ 1/2 results in a peak in the spectrum of primordial gravitational waves, which will be observable by the forthcoming LISA mission as well as by Advanced LIGO.

On rational points in CFT moduli spaces

Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there. We first study the bosonic sigma-model with S1 target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the S1 example, does not automatically follow from enhanced symmetry points being dense in the moduli space. We then explore the supersymmetric sigma-model on K3 by perturbing away from the torus orbifold locus. Though we do not reach a definite conclusion on the distribution of enhanced symmetry points in the K3 moduli space, we make several observations on how chiral currents can emerge and disappear under conformal perturbation theory.

Axion monodromy inflation, trapping mechanisms and the swampland

We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the swampland constraints. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the inflaton in a local minimum and leads to a graceful exit problem. On the other hand, the production of moduli fields at enhanced symmetry points can lead to a realization of trapped inflation consistent with the swampland constraints, as long as the coupling between the inflaton and the moduli fields is sufficiently large.

Quintessential inflation with a trap and axionic dark matter

We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling between the inflaton and the Peccei-Quinn (PQ) field which terminates the roll of the runaway inflaton and traps the latter at an enhanced symmetry point (ESP), thereby breaking the PQ symmetry. The kinetic density of the inflaton is transferred to the newly created thermal bath of the hot big bang due to the decay of PQ particles. The model successfully accounts for the observations of inflation and dark energy without any fine-tuning, while also resolving the strong CP problem of QCD and generating axionic dark matter, without isocurvature perturbations. Trapping the inflaton at the ESP ensures that the model does not suffer from the infamous 5th force problem, which typically plagues quintessence.

Particle production with left-right neutrino oscillations

When the Higgs field starts oscillation after Higgs inflation, gauge bosons are produced non-perturbatively near the Enhanced Symmetry Point (ESP). Just after the particle production, when the Higgs field is going away from the ESP, these gauge bosons gain mass and decay or annihilate into Standard Model (SM) fermions. Left-handed neutrinos can be generated in that way. If one assumes the see-saw mechanism, the mass matrix of a pair of left and right-handed neutrinos is non-diagonal. Although their mixing in the mass eigenstates is negligible in the true vacuum, it could be significant near the edge of the Higgs oscillation, where the off-diagonal component is large. Therefore, the left-handed neutrinos generated from the gauge bosons can start neutrino oscillation between the right-handed neutrinos. We study the particle production when such L-R neutrino oscillation is significant. For a working example, the non-thermal leptogenesis scenario after Higgs inflation is examined, which cannot be realized without the L-R neutrino oscillation. The same mechanism could be applied to other singlet particles whose abundance has been neglected.

Beauty is more attractive: particle production andmoduli trapping with higher dimensional interaction

We study quantum effects on moduli dynamics arising from particle production near the enhanced symmetry point (ESP). We focus on non-renormalizable couplings between the moduli field and the field that becomes light at the ESP. Considering higher dimensional interaction, we find that particle production is significant in a large area, which is even larger than the area that is expected from a renormalizable interaction. It is possible to find this possibility from a trivial adiabatic condition; however the quantitative estimation of particle production and trapping of the field in motion are far from trivial. In this paper we study particle production and trapping in detail, using both the analytical and numerical calculations, to find a clear and intuitive result that supports trapping in a vast variety of theories. Our study shows that trapping driven by a non-renormalizable interaction is possible. This possibility has not been considered in previous works. Some phenomenological models of particle physics will be mentioned to complement discussion.

Scalar trapping and Saxion cosmology

We study in detail the dynamics of a scalar field in thermal bath with symmetry breaking potential. In particular, we focus on the process of trapping of a scalar field at an enhanced symmetry point through the thermal/non-thermal particle production, taking into account the interactions of produced particles with the standard model particles. As an explicit example, we revisit the saxion dynamics with an initial amplitude much larger than the Peccei-Quinn scale and show that the saxion trapping phenomenon happens for the most cases and it often leads to thermal inflation. We also study the saxion dynamics after thermal inflation, and it is shown that thermal dissipation effect on the saxion can relax the axion overproduction problem from the saxion decay.

125 GeV Higgs boson and electroweak phase transition model classes

Recently, the ATLAS and CMS detectors have discovered a bosonic particle which, to a reasonable degree of statistical uncertainty, fits the profile of the Standard Model Higgs. One obvious implication is that models which predict a significant departure from Standard Model phenomenology, such as large exotic (e.g., invisible) Higgs decay or mixing with a hidden sector scalar, are already ruled out. This observation threatens the viability of electroweak baryogenesis, which favors, for example, a lighter Higgs and a Higgs coupled to or mixed with light scalars. To assess the broad impact of these constraints, we propose a scheme for classifying models of the electroweak phase transition and impose constraints on a class-by-class basis. We find that models, such as the MSSM, which rely on thermal loop effects are severely constrained by the measurement of a 125 GeV Higgs. Models which rely on tree-level effects from a light singlet are also restricted by invisible decay and mixing constraints. Moreover, we find that the parametric region favored by electroweak baryogenesis often coincides with an enhanced symmetry point with a distinctive phenomenological character. In particular, enhancements arising through an approximate continuous symmetry are phenomenologically disfavored, in contrast with enhancements from discrete symmetries. We also comment on the excess of diphoton events observed by ATLAS and CMS. We note that although Higgs portal models can accommodate both enhanced diphoton decay and a strongly first order electroweak phase transition, the former favors a negative Higgs portal coupling whereas the latter favors a positive one, and therefore these two constraints are at tension with one another.

Cosmological phases of the string thermal effective potential

In a superstring framework, the free energy density F can be determined unambiguously at the full string level once supersymmetry is spontaneously broken via geometrical fluxes. We show explicitly that only the moduli associated to the supersymmetry breaking may give relevant contributions. All other spectator moduli μ I give exponentially suppressed contributions for relatively small (as compared to the string scale) temperature T and supersymmetry breaking scale M. More concisely, for μ I > T and M, F takes the form F ( T , M ; μ I ) = F ( T , M ) + O [ exp ( − μ I T ) , exp ( − μ I M ) ] . We study the cosmological regime where T and M are below the Hagedorn temperature scale T H . In this regime, F remains finite for any values of the spectator moduli μ I . We investigate extensively the case of one spectator modulus μ d corresponding to R d , the radius-modulus field of an internal compactified dimension. We show that its thermal effective potential V ( T , M ; μ ) = F ( T , M ; μ ) admits five phases, each of which can be described by a distinct but different effective field theory. For late cosmological times, the Universe is attracted to a “Radiation-like evolution” with M ( t ) ∝ T ( t ) ∝ 1 / a ( t ) ∝ t − 2 / d . The spectator modulus μ ( t ) is stabilized either to the stringy enhanced symmetry point where R d = 1 , or fixed at an arbitrary constant μ 0 > T , M . For arbitrary boundary conditions at some initial time, t E , μ ( t ) may pass through more than one effective field theory phase before its final attraction.

Stabilizing moduli with thermal matter and nonperturbative effects

Even with recent progress, it is still very much an open question to understand how all compactification moduli are stabilized, since there are several mechanisms. For example, it is possible to generate a scalar potential either classically or through nonperturbative effects, such as gaugino condensation. Such a potential can stabilize certain of the moduli fields, for example, the dilaton. On the other hand, a background of thermal matter with moduli-dependent masses can also stabilize certain of the moduli, e.g., the radion. It is important to understand whether these two distinct mechanisms are compatible with each other, that is, that there are no interference terms that could spoil the moduli stabilization. In this paper, we study heterotic string theory on an $\mathcal{N}=1$ orbifold near an enhanced symmetry point. We then consider both a nonperturbatively generated potential and a gas of strings with moduli-dependent masses to stabilize the dilaton and radial modulus, respectively. We conclude that, given certain approximations, these two moduli stabilization mechanisms are compatible.

Trapped quintessential inflation in the context of flux compactifications

We present a model for quintessential inflation using a string modulus for theinflaton–quintessence field. The scalar potential of our model is based on genericnon-perturbative potentials arising in flux compactifications. We assume an enhancedsymmetry point (ESP), which fixes the initial conditions for slow roll inflation. Whencrossing the ESP the modulus becomes temporarily trapped, which leads to a brief stageof trapped inflation. This is followed by enough slow roll inflation to solve theflatness and horizon problems. After inflation, the field rolls down the potential andeventually freezes to a certain value because of cosmological friction. The latter is dueto the thermal bath of the hot big bang, which is produced by the decay of acurvaton field. The modulus remains frozen until the present, when it becomesquintessence.

Meta-stable dynamical supersymmetry breaking near points of enhanced symmetry

We show that metastable supersymmetry breaking is generic near certain enhanced symmetry points of gauge theory moduli spaces. Our model consists of two sectors coupled by a singlet and combines dynamical supersymmetry breaking with an O'Raifeartaigh mechanism in terms of confined variables. All relevant mass parameters, including the supersymmetry breaking scale, are generated dynamically. The metastable vacua appear as a result of a balance between non-perturbative and perturbative quantum effects along a pseudo-runaway direction.

Trapped quintessential inflation

Quintessential inflation is studied using a string modulus as the inflaton–quintessence field. The modulus begins its evolution at the steep part of its scalar potential, which is due to non-perturbative effects (e.g. gaugino condensation). It is assumed that the modulus crosses an enhanced symmetry point (ESP) in field space. Particle production at the ESP temporarily traps the modulus resulting in a brief period of inflation. More inflation follows, due to the flatness of the potential, since the ESP generates either an extremum (maximum or minimum) or a flat inflection point in the scalar potential. Eventually, the potential becomes steep again and inflation is terminated. After reheating the modulus freezes due to cosmological friction at a large value, such that its scalar potential is dominated by contributions due to fluxes in the extra dimensions or other effects. The modulus remains frozen until the present, when it can become quintessence and account for the dark energy necessary to explain the observed accelerated expansion.

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.

OPEN DESCENDANTS OF NAHE-BASED FREE FERMIONIC AND TYPE I ${\mathbb Z}_2^n$ MODELS

The NAHE set, that underlies the realistic free fermionic models, corresponds to ℤ2×ℤ2 orbifold at an enhanced symmetry point, with (h11,h21)=(27,3). Alternatively, a manifold with the same data is obtained by starting with a ℤ2×ℤ2 orbifold at a generic point on the lattice and adding a freely acting ℤ2 involution. In this paper we study type I orientifolds on the manifolds that underlie the NAHE-based models by incorporating such freely acting shifts. We present new models in the type I vacuum which are modulated by [Formula: see text] for n=2,3. In the case of n=2, the ℤ2×ℤ2 structure is a composite orbifold Kaluza–Klein shift arrangement. The partition function provides a simpler spectrum with chiral matter. For n=3, the case discussed is a ℤ2 modulation of the T6/ℤ2×ℤ2 spectrum. The additional projection shows an enhanced closed and open sector with chiral matter. The brane stacks are correspondingly altered from those which are present in the ℤ2×ℤ2 orbifold. In addition, we discuss the models arising from the open sector with and without discrete torsion.

Beauty is Attractive: Moduli Trapping at Enhanced Symmetry Points

We study quantum effects on moduli dynamics arising from the production of particles which are light at special points in moduli space. The resulting forces trap the moduli at these points, which often exhibit enhanced symmetry. Moduli trapping occurs in time-dependent quantum field theory, as well as in systems of moving D-branes, where it leads the branes to combine into stacks. Trapping also occurs in an expanding universe, though the range over which the moduli can roll is limited by Hubble friction. We observe that a scalar field trapped on a steep potential can induce a stage of acceleration of the universe, which we call trapped inflation. Moduli trapping ameliorates the cosmological moduli problem and may affect vacuum selection. In particular, rolling moduli are most powerfully attracted to the points with the largest number of light particles, which are often the points of greatest symmetry. Given suitable assumptions about the dynamics of the very early universe, this effect might help to explain why among the plethora of possible vacuum states of string theory, we appear to live in one with a large number of light particles and (spontaneously broken) symmetries. In other words, some of the surprising properties of our world might arise not through pure chance or miraculous cancellations, but through a natural selection mechanism during dynamical evolution.

Enhanced Gauge Symmetry and Braid Group Actions

Enhanced gauge symmetry appears in Type II string theory (as well as F- and M-theory) compactified on Calabi--Yau manifolds containing exceptional divisors meeting in Dynkin configurations. It is shown that in many such cases, at enhanced symmetry points in moduli a braid group acts on the derived category of sheaves of the variety. This braid group covers the Weyl group of the enhanced symmetry algebra, which itself acts on the deformation space of the variety in a compatible fashion. Extensions of this result are given for nontrivial $B$-fields on K3 surfaces, explaining physical restrictions on the $B$-field, as well as for elliptic fibrations. The present point of view also gives new evidence for the enhanced gauge symmetry content in the case of a local $A_{2n}$-configuration in a threefold having global $\Z/2$ monodromy.

Probing F-theory with branes

Last week, A. Sen found an explicit type I string compactification dual to the eight-dimensional F-theory construction with SO(8) 4 nonabelian gauge symmetry. He found that the perturbations around the enhanced symmetry point were described by the mathematics of the solution of N = 2, d = 4 SU(2) gauge theory with four flavors, and argued more generally that global symmetry enhancement in N = 2, d = 4 gauge theories corresponded to gauge symmetry enhancement in F-theory. We show that these N = 2, d = 4 gauge theories have a physical interpretation in the theory. They are the world-volume theories of 3-branes parallel to the 7-branes. They can be used to probe the structure of the exact quantum F-theory solutions. On the Higgs branch of the moduli space, the objects are equivalent to finite size instantons in the 7-brane gauge theory.

Compactifications of M-Theory to two dimensions

Compactifications of M-Theory to two dimensional space-time on (K3 × T 5)/ Z 2 and (K3 × K3 × S 1)/ Z 2 orientifolds are presented. These orientifolds provide examples of anomaly free chiral supergravity models in two dimensions with (8, 0) and (4, 0) supersymmetries. Anomaly free spectra at the enhanced symmetry points are also obtained. The results confirm the twisted sector contribution to the spectrum in the case of T 9/ Z 2 discussed earlier.