Scaling Symmetry Research Articles

Natural stabilization of the Higgs boson’s mass and alignment

Current data from the LHC indicate that the 125 GeV Higgs boson, $H$, is either the single Higgs of the Standard Model or, to a good approximation, an "aligned Higgs". We propose that $H$ is the pseudo-Goldstone dilaton of Gildener and Weinberg. Models based on their mechanism of scale symmetry breaking can naturally account for the Higgs boson's low mass and aligned couplings. We conjecture that they are the only way to achieve a "Higgslike dilaton" that is actually the Higgs boson. These models further imply the existence of additional Higgs bosons in the vicinity of 200 to about 550 GeV. We illustrate our proposal in a version of the two-Higgs-doublet model of Lee and Pilaftsis. Our version of this model is consistent with published precision electroweak and collider physics data. We describe tests to confirm, or exclude, this model at Run 3 of the LHC.

Nano, micro, and macro-scale effects on cochlear tuning

Reconciling the highly tuned and nonlinear basilar membrane (BM) response at the base with the nearly low-pass and weakly nonlinear response at the apex has presented a longstanding challenge to cochlear mechanics modelers. Recent experiments have shown that the BM centric view of cochlear mechanics is incomplete and have highlighted the importance of modeling and measuring the dynamics of the organ of Corti (OoC). Here, we describe a new computational model of the guinea pig cochlea that can correctly simulate the response at all frequencies. The model shows that the electromotile force from the outer hair cells modulate the differential motion between the reticular lamina and the BM. Model calculations at the apex show that the geometric taper of the scalae duct as well as the cytoarchitecture of the OoC breaks the scaling symmetry observed at the base. Further, the model predicts that the neural tuning at the base is primarily governed by the macroscopic dynamics of the cochlear partition, while the micro-scale fluid dynamics and the nano-scale channel dynamics dominate the neural tuning at the apex. Overall, the model provides a physiological explanation for the differences between high and low frequency hearing observed in psychophysical experiments. [Work supported by NIH-R01-04084.]

Scaling limits of dS vacua and the swampland

We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over α′ and string loop corrections.

A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere

We study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory. To this end, we consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a re-normalisation based on the integrated auto-correlation, the rate function one obtains at a given latitude by looking locally in space at long time averages agrees with what is obtained, instead, by looking locally in time at large spatial averages along the latitude. This is a result of scale symmetry in the spatio-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe the statistics of temporal averages of spatial averages performed over large spatial scales, thus allowing one to look into spatio-temporal large deviations. Finally, we find out that, as a result of a modification in the rate function, large deviations are relatively more likely to occur when looking at spatial averages performed over intermediate scales. This is due to the existence of weather patterns associated with the low-frequency variability of the atmosphere, which are responsible for extended and temporally persistent heat waves or cold spells. Extreme value theory is used to benchmark our results.

Scale hierarchies, symmetry breaking, and particle spectra in SU(3)-family extended SUSY trinification

A unification of left-right $\rm{SU}(3)_\rm{L}\times \rm{SU}(3)_\rm{R}$, colour $\rm{SU}(3)_\rm{C}$ and family $\rm{SU}(3)_\rm{F}$ symmetries in a maximal rank-8 subgroup of ${\rm{E}}_8$ is proposed as a landmark for future explorations beyond the Standard Model (SM). We discuss the implications of this scheme in a supersymmetric (SUSY) model based on the trinification gauge $\left[\rm{SU}(3)\right]^3$ and global $\rm{SU}(3)_\rm{F}$ family symmetries. Among the key properties of this model are the unification of SM Higgs and lepton sectors, a common Yukawa coupling for chiral fermions, the absence of the $\mu$-problem, gauge couplings unification and proton stability to all orders in perturbation theory. The minimal field content consistent with a SM-like effective theory at low energies is composed of one $\mathrm{E}_6$ $27$-plet per generation as well as three gauge and one family $\rm{SU}(3)$ octets inspired by the fundamental sector of ${\rm{E}}_8$. The details of the corresponding (SUSY and gauge) symmetry breaking scheme, multi-scale gauge couplings' evolution, and resulting effective low-energy scenarios are discussed.

Bifurcation of fixed points in a O(N)-symmetric ( 2+1 )-dimensional gauged Φ6 theory with a Chern-Simons term

We examine the phase structure of an Abelian Chern-Simons system with relativistic charged matter fields with a sixth-order potential. Using a large $N$ technique, we compute the quantum effective potential and the renormalization group function of the coupling to the next-to-leading order of the $1/N$ expansion in terms of the Chern-Simons coefficient. The model has a phase which exhibits spontaneous breaking of scale symmetry accompanied by a massless dilaton which is a Goldstone mode. We show that the beta function of the sextic coupling exhibits, at the next order in the $1/N$ expansion, nontrivial running that we analyze explicitly in terms of the Chern-Simons coefficient. Viewed as a dynamical system, the renormalization group (RG) flow exhibits a topological normal form of a generic one-dimensional system having a fold bifurcation. We demonstrate that the corresponding IR and UV fixed points, each describing a conformal phase of the theory, approach each other until they merge, giving rise to a scaling behavior similar to Berezinskii-Kosterlitz-Thouless phase transitions. Our study identifies a window in the parameter space of the Chern-Simons coefficient where the renormalization group flow has a stable infrared fixed point and where scale invariance is recovered. We also find that the Chern-Simons interaction modifies the scaling dimension of the operator crossing marginality at the bifurcation points.

Fourier representations in Bergman spaces

We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of such domains with respect to each of these three groups of symmetries. The Fourier series, Fourier integral and Mellin integral representations so obtained may be used to give representations of the Bergman kernels of these domains.

Scaling symmetry meets topology

Scaling symmetry meets topology

A new property of the electromagnetic/Yang–Mills-conformal gravity system in spherical symmetry

We find a new property in W2-conformal gravity in spherical symmetry. We demonstrate that the charge of the electromagnetic field varies with respect to the partial scaling symmetry (conformal transformations in subspaces of a spacetime) in the conformal gravity. We find that the electric and magnetic charges can vanish or appear via partial conformal transformations for the on-shell configurations in the conformal gravity. We find a solution of a Yang–Mills SU(2)-charged black hole in the conformal gravity, and further demonstrate that the SU(2) charge has similar properties with electromagnetic magnetic charges in the conformal gravity. We demonstrate how to imbed the electromagnetic and Yang–Mills SU(2) gauge field into the conformal gravity via such a symmetry. We make a brief discussion about the possibility to extend this argument to the Einstein gravity.

Gravitational waves from first-order phase transitions: LIGO as a window to unexplored seesaw scales

Within a recently proposed classically conformal model, in which the generation of neutrino masses is linked to spontaneous scale symmetry breaking, we investigate the associated phase transition and find it to be of strong first order with a substantial amount of supercooling. Carefully taking into account the vacuum energy of the meta-stable minimum, we demonstrate that a significant fraction of the model's parameter space can be excluded simply because the phase transition cannot complete. We argue this to be a powerful consistency check applicable to general theories based on classical scale invariance. Finally, we show that all remaining parameter points predict a sizable gravitational wave signal, so that the model can be fully tested by future gravitational wave observatories. In particular, most of the parameter space can already be probed by the upcoming LIGO science run starting in early 2019.

Pseudoconformal structure in dense baryonic matter

We clarify and extend further the idea developed in \cite{PKLMR,MLPR} that baryonic matter at high density has an emergent "pseudo-conformal symmetry." It is argued that as baryonic density exceeds $n \simeq n_{1/2} \gtrsim 2n_0$, a topology change mimicking the baryon-quark continuity takes place at $n_{1/2}$. In terms of skyrmions, this corresponds to the transition from skyrmions to half-skyrmions and impacts on the equation of state of dense baryonic matter. The emergence in medium at $n_{1/2}$ of parity-doublet symmetry -- which is invisible in QCD in matter-free vacuum -- plays the crucial role. The consequence of the topology change is that massive compact stars carry the "pseudo-conformal sound velocity" $v_s^2/c^2\approx 1/3$ at $n\gsim n_{1/2}$ signaling a precursor to precocious emergence of scale symmetry as well as {a} local symmetry hidden in QCD in the matter-free vacuum. A highly significant prediction of this work is that the topology change density from normal matter to half-skyrmion matter, up-to-date inaccessible either by QCD proper or by terrestrial experiments, could possibly be pinned down within the range $2 < n_{1/2}/n_0 < 4$, commensurate with the range expected for a continuous hadrons-to-quarks/gluons transition.

Scale symmetry and Weinberg's no-go theorem in the cosmological constant problem

We complete the proof of Weinberg's no-go theorem on the cosmological constant problem in classical gravity when the theory has a (global) scale symmetry. Stimulated with this proof, we explore a solution to the cosmological constant problem by the help of renormalization group equations. We find that the manifestly scale invariant regularization method provides a physically plausible solution to the cosmological constant problem, in particular, to the issue of radiative instability of the cosmological constant.

Scaling and Visualization of Nucleotide Sequences

Algorithms for scaling and visualization of nucleotide sequences developed in this study allow identifying relationships between the biochemical parameters of DNA and RNA molecules with scale invariance, fractal clusters, nonlinear ordering and symmetry and noise immunity of visual representations in orthogonal coordinate systems. The algorithms are capable of displaying structures of the nucleotide sequences of living organisms by visualizing them in spaces of various dimensions and scales. Approximately one hundred genes (protozoa, plants, fungi, animals, viruses) were analysed and examples of visualization of the nucleotide composition of genomes of various species have been presented. The developed method contributes to an in-depth understanding of the principles of genetic coding and simplifying the perception of genetic information due to the algorithmic interpretation of the basic properties of polynucleotide fragments with visualization of the final geometric structure of the genetic code.

Self-similar cuspidal formation by runaway thermocapillary forces in thin liquid films

Many physical systems give rise to dynamical behavior leading to cuspidal shapes which represent a singularity of the governing equation. The cusp tip often exhibits self-similarity as well, indicative of scaling symmetry invariant in time up to a change of scale. Cuspidal shapes even occur in liquid systems when the driving force for fluid elongation is sufficiently strong to overcome leveling by capillarity. In almost all cases reported in the literature, however, the moving interface is assumed to be shear-free and the operable forces orient exclusively in the direction normal to the advancing boundary. Here we focus on a system in which a slender liquid film is exposed to large thermocapillary stresses, a system previously shown to undergo a linear instability resembling microlens arrays. We demonstrate by analytic and numerical means how in the nonlinear regime runaway thermocapillary forces induce cuspidal formations terminated by a conical tip whose slope is given by an analytic relation. On a fundamental level, this finding broadens our understanding of known categories of flows that can generate cuspidal forms. More practically, the system examined here introduces a potentially novel lithographic method for one-step non-contact fabrication of cuspidal microarrays.

Dark energy density predicted and explained

It has recently been shown that the observed Hubble function for cosmological expansion can be fitted accurately back to redshift unity (7.33 Gyr ago) with only one free constant, while neglecting cosmic curvature and mass density, using the modified Friedmann equation implied by subjecting the Higgs scalar field model to conformal Weyl scaling symmetry. It is shown here that the implied dark energy parameter is produced by dressing the bare scalar field by the neutral gauge boson field induced by weak cosmological time dependence of the conformal Higgs model. Predicted persistent cosmic acceleration is consistent with the nonclassical acceleration parameter inferred by conformal theory from observed excessive galactic rotation velocities and dark galactic halos, all without dark matter.

Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci

In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic symmetries on the bifurcation behaviour of solutions to Hamiltonian boundary value problems. Under non-degeneracy conditions, a group action by conformal symplectic symmetries has the effect that the flow map cannot degenerate in a direction which is tangential to the action. This imposes restrictions on which singularities can occur in boundary value problems. Our results generalise classical results about conjugate loci on Riemannian manifolds to a large class of Hamiltonian boundary value problems with, for example, scaling symmetries.&#x0D;

CMF-iteMS: An automatic threshold selection for detection of copy-move forgery

Taking into consideration that the prior CMF detection methods rely on several fixed threshold values in the filtering process, we propose an efficient CMF detection method with an automatic threshold selection, named as CMF-iteMS. The CMF-iteMS recommends a PatchMatch-based CMF detection method that adapts Fourier-Mellin Transform (FMT) as the feature extraction technique while a new automatic threshold selection based on iterative means of regions size (iteMS) procedure is introduced to have flexibility in changing the threshold value for various characteristics (quality, sizes, and attacks) in each input image. To ensure the reliability of the proposed CMF-iteMS, the method is compared with four state-of-the-art CMF detection methods based on Scale Invariant Feature Transform (SIFT), patch matching, multi-scale analysis and symmetry techniques using three available datasets that cover the variety of characteristics in CMF images. The results show that the F-score of the CMF-iteMS outperformed existing CMF detection methods by exceeding an average of 90% F-score values for image-level evaluation and 82% of F-score value for pixel-level evaluation for all datasets in original size. As special attention is given to the image resizing attack, the method is able to maintain the highest performance even if the images in the datasets are resized to 0.25 parameter.

Asymptotic safety of scalar field theories

We study $3d$ $O(N)$ symmetric scalar field theories using Polchinski's renormalisation group. In the infinite $N$ limit the model is solved exactly including at strong coupling. At short distances the theory is described by a line of asymptotically safe ultraviolet fixed points bounded by asymptotic freedom at weak, and the Bardeen-Moshe-Bander phenomenon at strong sextic coupling. The Wilson-Fisher fixed point arises as an isolated low-energy fixed point. Further results include the conformal window for asymptotic safety, convergence-limiting poles in the complex field plane, and the phase diagram with regions of first and second order phase transitions. We substantiate a duality between Polchinski's and Wetterich's versions of the functional renormalisation group, also showing that that eigenperturbations are identical at any fixed point. At a critical sextic coupling, the duality is worked out in detail to explain the spontaneous breaking of scale symmetry responsible for the generation of a light dilaton. Implications for asymptotic safety in other theories are indicated.

Emergent Scale Invariance and Climate Sensitivity

Earth’s global surface temperature shows variability on an extended range of temporal scales and satisfies an emergent scaling symmetry. Recent studies indicate that scale invariance is not only a feature of the observed temperature fluctuations, but an inherent property of the temperature response to radiative forcing, and a principle that links the fast and slow climate responses. It provides a bridge between the decadal- and centennial-scale fluctuations in the instrumental temperature record, and the millennial-scale equilibration following perturbations in the radiative balance. In particular, the emergent scale invariance makes it possible to infer equilibrium climate sensitivity (ECS) from the observed relation between radiative forcing and global temperature in the instrumental era. This is verified in ensembles of Earth system models (ESMs), where the inferred values of ECS correlate strongly to estimates from idealized model runs. For the range of forcing data explored in this paper, the method gives best estimates of ECS between 1.8 and 3.7 K, but statistical uncertainties in the best estimates themselves will provide a wider likely range of the ECS.

Conservation laws for a generalized seventh order KdV equation

In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined x - and t - translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation.