Scaling Symmetry Research Articles

An observation-based scaling model for climate sensitivity estimates and global projections to 2100

We directly exploit the stochasticity of the internal variability, and the linearity of the forced response to make global temperature projections based on historical data and a Green’s function, or Climate Response Function (CRF). To make the problem tractable, we take advantage of the temporal scaling symmetry to define a scaling CRF characterized by the scaling exponent H, which controls the long-range memory of the climate, i.e. how fast the system tends toward a steady-state, and an inner scale tau approx 2 years below which the higher-frequency response is smoothed out. An aerosol scaling factor and a non-linear volcanic damping exponent were introduced to account for the large uncertainty in these forcings. We estimate the model and forcing parameters by Bayesian inference which allows us to analytically calculate the transient climate response and the equilibrium climate sensitivity as: 1.7^{+0.3} _{-0.2} K and 2.4^{+1.3} _{-0.6} K respectively (likely range). Projections to 2100 according to the RCP 2.6, 4.5 and 8.5 scenarios yield warmings with respect to 1880–1910 of: 1.5^{+0.4}_{-0.2}K, 2.3^{+0.7}_{-0.5} K and 4.2^{+1.3}_{-0.9} K. These projection estimates are lower than the ones based on a Coupled Model Intercomparison Project phase 5 multi-model ensemble; more importantly, their uncertainties are smaller and only depend on historical temperature and forcing series. The key uncertainty is due to aerosol forcings; we find a modern (2005) forcing value of [-1.0, -0.3], ,,mathrm{Wm} ^{-2} (90 % confidence interval) with median at -0.7 ,,mathrm{Wm} ^{-2}. Projecting to 2100, we find that to keep the warming below 1.5 K, future emissions must undergo cuts similar to RCP 2.6 for which the probability to remain under 1.5 K is 48 %. RCP 4.5 and RCP 8.5-like futures overshoot with very high probability.

EXACT SCALE INVARIANCE IN THE ERA OF THE BIG BANG BEGINNING AS A PROBLEM OF FUNDAMENTAL PHYSICS

Based on the ideas of E. Harrison and Ya.B. Zel’dovich, a hypothesis is formulated on the exact scale symmetry of the Universe in the era of the Big Bang beginning and on the cause of the Big Bang as a spontaneous violation of exact scale invariance. It is argued that this concept of exact scale symmetry is a challenge to modern concepts of fundamental physics in the mathematical, physical, cosmological, quantum-mechanical and metaphysical aspects. Each of the aspects is analyzed.

Heavy light inflaton and dark matter production

We study the minimal extension of the SM by a scalar with quartic interaction serving as an inflaton. For the model where scale symmetry is broken only in the inflaton sector, the mass of the inflaton is constrained to be relatively low. Here, we analysed the previously omitted situation of the inflaton masses $m_{\chi}\gtrsim 250\text{ GeV}$. Therefore, we provide a window of inflaton masses with viable inflationary properties that evade direct observational constraints, due to their small mixing with the Higgs sector. The addition of heavy neutral leptons with Majorana masses induced by the interaction with the inflaton allow for Cold Dark Matter in the model with masses $O(1-10)\text{ MeV}$.

Palatini quadratic gravity: spontaneous breaking of gauged scale symmetry and inflation

We study quadratic gravity R^2+R_{[mu nu ]}^2 in the Palatini formalism where the connection and the metric are independent. This action has a gauged scale symmetry (also known as Weyl gauge symmetry) of Weyl gauge field v_mu = (tilde{Gamma }_mu -Gamma _mu )/2, with tilde{Gamma }_mu (Gamma _mu ) the trace of the Palatini (Levi-Civita) connection, respectively. The underlying geometry is non-metric due to the R_{[mu nu ]}^2 term acting as a gauge kinetic term for v_mu . We show that this theory has an elegant spontaneous breaking of gauged scale symmetry and mass generation in the absence of matter, where the necessary scalar field (phi ) is not added ad-hoc to this purpose but is “extracted” from the R^2 term. The gauge field becomes massive by absorbing the derivative term partial _mu ln phi of the Stueckelberg field (“dilaton”). In the broken phase one finds the Einstein–Proca action of v_mu of mass proportional to the Planck scale Msim langle phi rangle , and a positive cosmological constant. Below this scale v_mu decouples, the connection becomes Levi-Civita and metricity and Einstein gravity are recovered. These results remain valid in the presence of non-minimally coupled scalar field (Higgs-like) with Palatini connection and the potential is computed. In this case the theory gives successful inflation and a specific prediction for the tensor-to-scalar ratio 0.007le rle 0.01 for current spectral index n_s (at 95% CL) and N=60 efolds. This value of r is mildly larger than in inflation in Weyl quadratic gravity of similar symmetry, due to different non-metricity. This establishes a connection between non-metricity and inflation predictions and enables us to test such theories by future CMB experiments.

Counterdiabatic control of transport in a synthetic tight-binding lattice

Quantum state transformations that are robust to experimental imperfections are important for applications in quantum information science and quantum sensing. Counterdiabatic (CD) approaches, which use knowledge of the underlying system Hamiltonian to actively correct for diabatic effects, are powerful tools for achieving simultaneously fast and stable state transformations. Protocols for CD driving have thus far been limited in their experimental implementation to discrete systems with just two or three levels, as well as bulk systems with scaling symmetries. Here, we extend the tool of CD control to a discrete synthetic lattice system composed of as many as nine sites. Although this system has a vanishing gap and thus no adiabatic support in the thermodynamic limit, we show that CD approaches can still give a substantial, several order-of-magnitude, improvement in fidelity over naive, fast adiabatic protocols.

Principal factors in performance of indirect-drive laser fusion experiments

Progress in inertial confinement fusion depends on the accurate interpretation of experiments that are complex and difficult to explain with simulations. Results could depend on small changes in the laser pulse or target or physics that are not fully understood or characterized. In this paper, we discuss an x-ray-driven platform [Baker et al., Phys. Rev. Lett. 121, 135001 (2018)] with fewer sources of degradation and find the fusion yield can be described as a physically motivated function of laser energy, target scale, and implosion symmetry. This platform and analysis could enable a more experimental approach to the study and optimization of implosion physics.

The holographic p + ip solution failed to win the competition in dRGT massive gravity

In this paper, the holographic p-wave superfluid model with charged complex vector field is studied in dRGT massive gravity beyond the probe limit. The stability of p-wave and p + ip solutions are compared in the grand canonical ensemble. The p-wave solution always get lower value of grand potential than the p + ip solution, showing that the holographic system still favors an anisotropic (p-wave) solution even with considering a massive gravity theory in bulk. In the holographic superconductor models with dRGT massive gravity in bulk, a key scaling symmetry is found to be violated by fixing the reference metric parameter c_0. Therefore, in order to get the dependence of condensate and grand potential on temperature, different values of horizon radius should be considered in numerical work. With a special choice of model parameters, we further study the dependence of critical back-reaction strength on the graviton mass parameter, beyond which the superfluid phase transition become first order. We also give the dependence of critical temperature on the back reaction strength b and graviton mass parameter m^2.

Similarity solutions for a class of Fractional Reaction-Diffusion equation

This work studies exact solvability of a class of fractional reaction-diffusion equation with the Riemann-Liouville fractional derivatives on the half-line in terms of the similarity solutions. We derived the conditions for the equation to possess scaling symmetry even with the fractional derivatives. Relations among the scaling exponents are determined, and the appropriate similarity variable introduced. With the similarity variable we reduced the differential partial differential equation to a fractional ordinary differential equation. Exactly solvable systems are then identified by matching the resulted ordinary differential equation with the known exactly solvable fractional ones. Several examples involving the three-parameter Mittag-Leffler function (Kilbas-Saigo function) are presented. The models discussed here turn out to correspond to superdiffusive systems.

Gapped dilatons in scale invariant superfluids

We study a paradigmatic model in field theory where a global $U(1)$ and scale symmetries are jointly and spontaneously broken. At zero density the model has a non-compact flat direction, which at finite density needs to be slightly lifted. The resulting low-energy spectrum is composed by a standard gapless $U(1)$ Nambu-Goldstone mode and a light dilaton whose gap is determined by the chemical potential and corrected by the couplings. Even though $U(1)$ and scale symmetries commute, there is a mixing between the $U(1)$ Nambu-Goldstone and the dilaton that is crucial to recover the expected dynamics of a conformal fluid and leads to a phonon propagating at the speed of sound. The results rely solely on an accurate study of the Ward-Takahashi identities and are checked against standard fluctuation computations. We extend our results to a boosted superfluid, and comment the relevance of our findings to condensed matter applications.

Renewable Energy System on Frequency Stability Control Strategy Using Virtual Synchronous Generator

This study constructs a novel virtual synchronous generator system based on a transfer function, and optimizes the parameters of the model by using the improved whale algorithm to improve the frequency control ability of virtual synchronous generator. Virtual synchronous generator technology helps to solve the problem that the integration of large-scale renewable energy generation into the power system leads to the deterioration of system frequency stability. It can maintain the symmetry of grid-connected scale and system stability. The virtual synchronous generator technology makes the inverter to have the inertia and damping characteristics of a synchronous generator. The inverter has the inertia characteristics and damps to reduce the frequency instability of high penetration renewable energy power system. The improved whale algorithm is efficient to find the best combination of control parameters and the effectiveness of the algorithm is verified by microgrid and power system. The results show that the proposed frequency coordination control scheme suppresses the frequency deviation of power system and keep the system frequency in a reasonable range.

Origin of ultra-light fields during inflation and their suppressed non-Gaussianity

We study the structure of multi-field inflation models where the primordial curvature perturbation is able to vigorously interact with an ultra-light isocurvature field — a massless fluctuation orthogonal to the background inflationary trajectory in field space. We identify a class of inflationary models where ultra-light fields can emerge as a consequence of an underlying “scaling transformation” that rescales the entire system's action and keeps the classical equations of motion invariant. This scaling invariance ensures the existence of an ultra-light fluctuation that freezes after horizon crossing. If the inflationary trajectory is misaligned with respect to the scaling symmetry direction, then the isocurvature field is proportional to this ultra-light field, and becomes massless. In addition, we find that even if the isocurvature field interacts strongly with the curvature perturbation — transferring its own statistics to the curvature perturbation — it is unable to induce large non-Gaussianity. The reason is simply that the same mechanism ensuring a suppressed mass for the isocurvature field is also responsible for suppressing its self-interactions. As a result, in models with light isocurvature fields the bispectrum is generally expected to be slow-roll suppressed, but with a squeezed limit that differs from Maldacena's consistency relation.

Quenched g_{A} in Nuclei and Emergent Scale Symmetry in Baryonic Matter.

The recent RIKEN experiment on the quenched g_{A} in the superallowed Gamow-Teller transition from ^{100}Sn indicates the role of scale anomaly encoded in the anomalous dimension β^{'} of the gluonic stress tensor Tr G_{μν}^{2}. This observation provides support to the notion of hidden scale symmetry emerging by strong nuclear correlations with an infrared (IR) fixed point realized-in the chiral limit-in the Nambu-Goldstone mode. We suggest there is an analogy in the way scale symmetry manifests in a nuclear medium to the continuity from the unitarity limit at low density (in light nuclei) to the dilaton limit at high density (in compact stars). In between the limits, say, at normal nuclear matter density, the symmetry is not visible, hence hidden.

Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typically exhibits memory effects. Recent work has found a variety of data-driven model reduction methods to be effective for representing such non-Markovian dynamics, but their scope and dynamical underpinning remain incompletely understood. Here, we study data-driven model reduction from a dynamical systems perspective. For both chaotic and randomly-forced systems, we show the problem can be naturally formulated within the framework of Koopman operators and the Mori-Zwanzig projection operator formalism. We give a heuristic derivation of a NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous input) model from an underlying dynamical model. The derivation is based on a simple construction we call Wiener projection, which links Mori-Zwanzig theory to both NARMAX and to classical Wiener filtering. We apply these ideas to the Kuramoto-Sivashinsky model of spatiotemporal chaos and a viscous Burgers equation with stochastic forcing.

Supersymmetric warped conformal field theory

In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that within a chiral superspace $(x^+,\th)$, a two-dimensional field theory with two translational invariance and a chiral scaling symmetry can have enhanced local symmetry, under the assumption that the dilation spectrum is discrete and non-negative. Similar to the pure bosonic case, there are two kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field theories, while the other being $N=1$ supersymmetric warped conformal field theories (SWCFT). We study the properties of SWCFT, including the representations of the algebra, the space of states and the correlation functions of the superprimaries.

UV Shadows in EFTs: Accidental Symmetries, Robustness and No‐Scale Supergravity

AbstractWe argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no‐scale supergravities in low‐energy 4D EFTs. We identify 4 nested types of no‐scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no‐scale properties (including non‐supersymmetric flat directions). We use these ideas to classify corrections to the low‐energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. Our prediction for the Kähler potential at any fixed order in and string loops agrees with all extant calculations. p‐form fields play two important roles: they spawn many (generalised) shift symmetries; and space‐filling 4‐forms teach 4D physics about higher‐dimensional phenomena like flux quantisation. We argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models.

Quantum Hall effective action for the anisotropic Dirac semimetal

We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise an expansion procedure that leads to a low-energy effective action consistent with the discrete $PT$ symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.

Weyl scaling invariant R2 gravity for inflation and dark matter

Inflation in the early universe can generate the nearly conformal invariant fluctuation that leads to the structures we observe at the present. The simple viable Starobinsky R2 inflation has an approximate global scale symmetry. We study the conformal symmetric Weyl Rˆ2 and general F(Rˆ) theories and demonstrate their equivalence to Einstein gravity coupled with a scalar and a Weyl gauge field. The scalar field in Weyl Rˆ2 gravity can be responsible for inflation with Starobinsky model as the attractor, potentially distinguishable from the latter by future experiments. The intrinsic Weyl gauge boson becomes massive once the Einstein frame is fixed, and constitutes as a dark matter candidate with mass up to ∼5×1016GeV.

A perceptually optimised bivariate visualisation scheme for high-dimensional fold-change data

Visualising data as diagrams using visual attributes such as colour, shape, size, and orientation is challenging. In particular, large data sets demand graphical display as an essential step in the analysis. In order to achieve comprehension often different attributes need to be displayed simultaneously. In this work a comprehensible bivariate, perceptually optimised visualisation scheme for high-dimensional data is proposed and evaluated. It can be used to show fold changes together with confidence values within a single diagram. The visualisation scheme consists of two parts: a uniform, symmetric, two-sided colour scale and a patch grid representation. Evaluation of uniformity and symmetry of the two-sided colour scale was performed in comparison to a standard RGB scale by twenty-five observers. Furthermore, the readability of the generated map was validated and compared to a bivariate heat map scheme.

Unified interpretation of scalegenesis in conformally extended standard models: a dynamical origin of Higgs portal * * Supported in part by the National Science Foundation of China (NSFC) (11747308), the Seeds Funding of Jilin University (S.M.). H.I. and R.O. thank for the hospitality of Center for Theoretical Physics and College of Physics, Jilin University where the present work has been

We present a universal interpretation of a class of conformal extended standard models that include Higgs portal interactions as realized in low-energy effective theories. The scale generation mechanism in this class (scalegenesis) arises along the (nearly) conformal/flat direction for breaking scale symmetry, where the electroweak symmetry-breaking structure arises similarly as in the standard model. A dynamical origin for the Higgs portal coupling can provide the discriminator for the low-energy “universality class,” to be probed in forthcoming collider experiments.

Restricted Weyl symmetry

We discuss the physics of a restricted Weyl symmetry in a curved space-time where a gauge parameter $\Omega(x)$ of Weyl transformation satisfies a constraint $\Box \Omega = 0$. First, we present a model of QED where we have a restricted gauge symmetry in the sense that a $U(1)$ gauge parameter $\theta(x)$ obeys a similar constraint $\Box \theta = 0$ in a flat Minkowski space-time. Next, it is precisely shown that a global scale symmetry must be spontaneously broken at the quantum level. Finally, we discuss the origin of the restricted Weyl symmetry and show that its symmetry can be derived from a full Weyl symmetry by taking a gauge condition $R = 0$ in the BRST formalism.