Renormalization Group Research Articles

Time evolution and thermal renormalization group flow in cosmology

Time-evolution of the Universe as described by the Friedmann equation can be coupled to equations of motion of matter fields. Quantum effects may be incorporated to improve these classical equations of motion by the renormalization group (RG) running of their couplings. Since temporal and thermal evolutions are linked to each other, astrophysical and cosmological treatments based on zero-temperature RG methods require the extension to finite-temperatures. We propose and explore a modification of the usual finite-temperature RG approach by relating the temperature parameter to the running RG scale as T≡kT=τk (in natural units), where kT is acting as a running cutoff for thermal fluctuations and the momentum k can be used for the quantum fluctuations. In this approach, the temperature of the expanding universe is related to the dimensionless quantity τ (and not to kT). We show that by this choice dimensionless RG flow equations have no explicit k-dependence, as it is convenient. We also discuss how this modified thermal RG is used to handle high-energy divergences of the RG running of the cosmological constant and to “solve the triviality” of the ϕ4 model by a thermal phase transition in terms of τ in d=4 Euclidean dimensions.

There’s plenty of room in the middle: The unsung revolution of the renormalization group

The remarkable technical contributions of Michael E. Fisher to statistical physics and the development of the renormalization group are widely known and deeply influential. But less well known is his early and profound appreciation of the way in which renormalization group created a revolution in our understanding of how physics — in fact, all science — is practiced and the concomitant adjustment that needs to be made to our conception of the purpose and philosophy of science. In this chapter, I attempt to redress this imbalance, with examples from Fisher’s writings and my own work. It is my hope that this tribute will help remove some of the confusion that surrounds the scientific usage of minimal models and renormalization group concepts, as well as their limitations, in the ongoing effort to understand emergence in complex systems.

Comparing how compost and manure affect soil organic matter using a complete factorial design

BackgroundThe aim of this study was to determine the influence of physico-chemical factors on soil organic matter by comparing two types of soil improver: one produced from olive mill waste cake residues (CRPM) and the other from manure (CF). This was achieved using Full Factorial Design, the main objective of which is to measure precisely the impact of each factor on a given response, to analyze the interactions between the various factors and to identify the optimum conditions for achieving a specific objective or improving the performance of a process. MethodsFour independent factors were studied: pH, electrical conductivity, humidity and carbon/nitrogen (C/N) ratio. Using design, based on their significance, coefficient of determination, analysis of variance and Pareto charts, the interactions between these variables were assessed to identify those with the most positive impact on soil fertility. ResultsThe results show that, for CRPM compost, the most positive interaction is between pH and ratio C/N. For manure, the interaction between pH and moisture has the greatest beneficial effect. These findings underline the importance of controlling all three factors − pH, moisture and ratio C/N to optimize soil fertility. ConclusionsThe analysis confirmed the reliability of the models used, with p-values below 0.05 and coefficients of determination (R2 and adjusted R2) close to 1, indicating the robustness of the models. Pareto diagrams were used to precisely identify the most relevant interactions for improving soil amendment management.

Drug Interactions between Androgen Receptor Axis-Targeted Therapies and Antithrombotic Therapies in Prostate Cancer: Delphi Consensus.

Background/Objectives: Abiraterone acetate, apalutamide, darolutamide, and enzalutamide, which make up the androgen receptor axis-targeted therapies (ARATs) drug class, are commonly used in the management of prostate cancer. Many patients on ARATs also receive oral antithrombotic therapy (i.e., anticoagulants or antiplatelets). The concomitant use of ARATs and antithrombotic therapies creates the potential for clinically relevant drug-drug interactions, but the literature regarding the actual consequences of these interactions, and guidance for co-prescribing, is limited. We assembled a multidisciplinary panel of experts and provided them with clinical information derived from a comprehensive literature review regarding the drug-drug interactions between ARATs and antithrombotic therapies. Methods: A three-stage modified electronic Delphi process was used to gather and consolidate opinions from the panel. Each stage consisted of up to three rounds of voting to achieve consensus on which ARAT/antithrombotic therapy drug pairs warrant attention, the possible clinical consequences of drug-drug interactions, and suggested actions for management. Results: The panel achieved consensus to avoid 11 ARAT/antithrombotic therapy drug pairs and modify therapy for eight pairs. Assessments relied heavily on pharmacokinetic data and extrapolation from drug-drug interaction studies of similarly metabolized drugs. Conclusions: This e-Delphi process highlights the need for further research into the clinical impact of ARAT/antithrombotic drug interactions. Nonetheless, the suggested actions aim to provide clinicians with a practical framework for therapeutic decision making.

The biogeographic patterns of the olive fly and its primary symbiont Candidatus Erwinia dacicola across the distribution area of the olive tree.

The olive fly, Bactrocera oleae (Rossi, 1790), is the major insect pest of olives attacking both cultivated and wild olive. Bactrocera oleae carries a primary and vertically transmitted symbiont, the bacterium Candidatus Erwinia dacicola. As any primary symbiont, it plays an important role in the reproduction and lifespan of the fly. The genetic 16S rRNA diversity of the primary symbiont and the mitochondrial haplotype variation of the insect host were simultaneously examined in 54 olive fly populations. The aim was to unravel the biogeographic patterns of this economically relevant host-bacteria interaction across a wide distribution area. Three symbiont haplotypes were identified. The primary symbiont showed a lower haplotype diversity than that of its host, a characteristic indicative of a long-term interaction. A significant genetic and geographic association between host and primary symbiont was observed, with an East-West genetic differentiation pattern in the Mediterranean basin, coinciding with the historical genetic distribution of the olive tree. The study shows promise, informing and aiding the development of future tools for the control of the olive fly.

Efficient simulation of open quantum systems coupled to a reservoir through multiple channels.

It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system-bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system-bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system-bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system-bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system-bath couplings using matrix product states, which may further our understanding of nonlocal exciton-phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group

Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group

Sensitivity to kaon decays to ALPs at fixed target experiments

We study the sensitivity of fixed target experiments to hadronically coupled axionlike particles (ALPs) produced in kaon decays, with a particular emphasis on current and upcoming Short-Baseline Neutrino (SBN) experiments. We demonstrate that below the kaon decay mass threshold (ma<mK−mπ) kaon decay is the dominant production mechanism for ALPs at neutrino experiments, larger by many orders of magnitude than production in pseudoscalar mixing. Such axions can be probed principally by the diphoton and dimuon final states. In the latter case, even if the axion does not couple to muons at tree level, such a coupling is induced by the renormalization group flow from the UV scale. We reinterpret prior results by CHARM and MicroBooNE through these channels and show that they constrain new areas of heavy axion parameter space. We also show projections of the sensitivity of the SBN experiment and Deep Underground Neutrino Experiment (DUNE) to axions through these channels, which reach up to a decade higher in the axion decay constant beyond existing constraints. DUNE projects to have a sensitivity competitive with other world-leading upcoming experiments. Published by the American Physical Society 2024

Algebraic structure of the renormalization group in the renormalizable QFT theories

In this paper, we consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant, its generators [Formula: see text] with [Formula: see text] satisfy the commutation relations of the Witt algebra and, therefore, form its subalgebra. The commutation relations are also written for the more general case when finite renormalizations are made for both the coupling constant and matter fields. We also construct the generator of the Abelian subgroup corresponding to the changes of the renormalization scale. The explicit expressions for the renormalization group generators are written in the case when they act on the [Formula: see text]-function and the anomalous dimension. It is explained how the finite changes of these functions under the finite renormalizations can be obtained with the help of the exponential map.

Holographic Lifshitz flows

Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or ‘Lifshitz’) exponent z. Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as the flow from a z = 1 UV fixed point to a z = 2 IR fixed point. In strongly coupled theories, there are good arguments suggesting that Lorentz invariance can emerge dynamically in the IR from a Lorentz violating UV. In this work, we perform a generic study of fixed points and the possible RG flows among them in a minimal bottom-up holographic model without Lorentz invariance, aiming to shed light on the possible options and the related phenomenology. We find: i) A minor generalization of previous models involving a massive vector field with allowed self-couplings leads to a much more efficient emergence of Lorentz invariance than in the previous attempts. Moreover, we find that generically the larger is the UV dynamical exponent zUV the faster is the recovery of Lorentz symmetry in the IR. ii) We construct explicitly a holographic model with a line of fixed points, realizing different Lifshitz scaling along the line. iii) We also confirm the monotonicity of a recently proposed a-function along all our Lorentz violating RG flows.

Explicit entropic proofs of irreversibility theorems for holographic RG flows

We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the c-, F -, and a-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic c-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: there, we reprove the monotonicity of flows from AdSD+1 to AdS3 and prove the novel case of flows from AdS5 to AdS4.

Gas–Liquid Mixability Study in a Jet-Stirred Tank for Mineral Flotation

Micro- and nano-bubble jet stirring, as an emerging technology, shows great potential in complex mineral sorting. Flow field characteristics and structural parameters of the gas–liquid two-phase system can lead to uneven bubble distribution inside the reaction vessel. Gas–liquid mixing uniformity is crucial for evaluating stirring effects, as increasing the contact area enhances reaction efficiency. To improve flotation process efficiency and resource recovery, further investigation into flow field characteristics and structural optimization is necessary. The internal flow field of the jet-stirred tank was analyzed using computational fluid dynamics (CFDs) with the Eulerian multiphase flow model and the Renormalization Group (RNG) k − ε turbulence model. Various operating (feeding and aerating volumes) and structural parameters (nozzle direction, height, inner diameter, and radius ratio) were simulated. Dimensionless variance is a statistical metric used to assess gas–liquid mixing uniformity. The results indicated bubbles accumulated in the middle of the vessel, leading to uneven mixing. Lower velocities resulted in low gas volume fractions, while excessively high velocities increased differences between the center and near-wall regions. Optimal mixing uniformity was achieved with a circumferential nozzle direction, 80 mm height, 5.0 mm inner diameter, and 0.55 radius ratio.

Nematic Superconductivity and Its Critical Vestigial Phases in the Quasicrystal.

We propose a general mechanism to realize nematic superconductivity (SC) and reveal its exotic vestigial phases in the quasicrystal (QC). Starting from a Penrose-Hubbard model, our microscopic studies suggest that the Kohn-Luttinger mechanism driven SC in the QC is usually gapless due to violation of Anderson's theorem, rendering that both chiral and nematic SCs are common. The nematic SC in the QC can support novel vestigial phases driven by pairing phase fluctuations above its T_{c}. Our combined renormalization group and MonteCarlo studies provide a phase diagram in which, besides the conventional charge-4e SC, two critical vestigial phases emerge, i.e., the quasinematic (QN) SC and QN metal. In the two QN phases, discrete lattice rotation symmetry is counterintuitively "quasibroken" with power-law decaying orientation correlation. They separate the phase diagram into various phases connected via Berezinskii-Kosterlitz-Thouless (BKT) transitions. These remarkable critical vestigial phases, which resemble the intermediate BKT phase in the q state (q≥5) clock model, are a consequence of the fivefold (or higher) anisotropy field brought about by the unique QC symmetry, which are absent in conventional crystalline materials.

Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna

We have studied numerically the Lee-Yang singularities of the four dimensional Ising model at criticality, which is believed to be in the same universality class as the φ44 scalar field theory. We have focused in the numerical characterization of the logarithmic corrections to the scaling of the zeros of the partition function and its cumulative probability distribution, finding a very good agreement with the predictions of the renormalization group computation on the φ44 scalar field theory. To obtain these results, we have extended a previous study [R. Kenna, C. B. Lang, Nucl. Phys., 1993, B393, 461] in which there were computed numerically the first two zeros for L≤24 lattices, to the computation of the first four zeros for L≤64 lattices.

Favorable phase transitions induced by spinful electron–electron interactions in two-dimensional semimetal with a quadratic band crossing point

We study the effects of marginally spinful electron–electron interactions on the low-energy instabilities and favorable phase transitions in a two-dimensional (2D) spin-1/2 semimetal that owns a quadratic band crossing point (QBCP) parabolically touched by the upper and lower bands. In the framework of a renormalization group procedure, all sorts of interactions are treated on the equal footing to derive the coupled energy-dependent evolutions of all interaction couplings that govern the low-energy properties. Deciphering the essential physical information of such flows, we at first find that the tendencies of interaction parameters fall into three categories including Limit case, Special case, and General case based on the initial conditions. In addition, the 2D QBCP system is attracted to several distinct kinds of fixed points (FPs) in the interaction-parameter space, namely FP1+/FP2−, FP1±/ FP2±/FP3±, and FP1±/FP3±/FP41,42,43± with the subscripts characterizing the features of FPs for the Limit, Special, and General cases, respectively. Furthermore, as approaching these FPs, we demonstrate that the spinful fermion–fermion interactions can induce a number of favorable instabilities accompanied by certain phase transitions. Specifically, the quantum anomalous Hall (QAH), quantum spin Hall (QSH), and nematic (Nem.) site(bond) states are dominant for FP1±, FP2±, and FP3±, respectively. Rather, QSH becomes anisotropic nearby FP41,42,43± with one component leading and the others subleading. Besides, Nem.site(bond), chiral superconductivity, and nematic-spin-nematic (NSN.) site(bond) are subleading candidates around these FPs. Our findings provide valuable insights for further research into the 2D QBCP and similar systems.

DMRG study of the theta-dependent mass spectrum in the 2-flavor Schwinger model

We study the θ-dependent mass spectrum of the massive 2-flavor Schwinger model in the Hamiltonian formalism using the density-matrix renormalization group (DMRG). The masses of the composite particles, the pion and sigma meson, are computed by two independent methods. One is the improved one-point-function scheme, where we measure the local meson operator coupled to the boundary state and extract the mass from its exponential decay. Since the θ term causes a nontrivial operator mixing, we unravel it by diagonalizing the correlation matrix to define the meson operator. The other is the dispersion-relation scheme, a heuristic approach specific to Hamiltonian formalism. We obtain the dispersion relation directly by measuring the energy and momentum of the excited states. The sign problem is circumvented in these methods, and their results agree with each other even for large θ. We reveal that the θ-dependence of the pion mass at m/g = 0.1 is consistent with the prediction by the bosonized model. We also find that the mass of the sigma meson satisfies the semi-classical formula, Mσ/Mπ = 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{3} $$\\end{document}, for almost all region of θ. While the sigma meson is a stable particle thanks to this relation, the eta meson is no longer protected by the G-parity and becomes unstable for θ ≠ 0.

Extremal fixed points and Diophantine equations

The coupling constants of fixed points in the ϵ expansion at one loop are known to satisfy a quadratic bound due to Rychkov and Stergiou. We refer to fixed points that saturate this bound as extremal fixed points. The theories which contain such fixed points are those which undergo a saddle-node bifurcation, entailing the presence of a marginal operator. Among bifundamental theories, a few examples of infinite families of such theories are known. A necessary condition for extremality is that the sizes of the factors of the symmetry group of a given theory satisfy a specific Diophantine equation, given in terms of what we call the extremality polynomial. In this work we study such Diophantine equations and employ a combination of rigorous and probabilistic estimates to argue that these infinite families constitute rare exceptions. The Pell equation, Falting’s theorem, Siegel’s theorem, and elliptic curves figure prominently in our analysis. In the cases we study here, more generic classes of multi-fundamental theories saturate the Rychkov-Stergiou bound only in sporadic cases or in limits where they degenerate into simpler known examples.

Bioinformatics approaches for studying molecular sex differences in complex diseases.

Many complex diseases exhibit pronounced sex differences that can affect both the initial risk of developing the disease, as well as clinical disease symptoms, molecular manifestations, disease progression, and the risk of developing comorbidities. Despite this, computational studies of molecular data for complex diseases often treat sex as a confounding variable, aiming to filter out sex-specific effects rather than attempting to interpret them. A more systematic, in-depth exploration of sex-specific disease mechanisms could significantly improve our understanding of pathological and protective processes with sex-dependent profiles. This survey discusses dedicated bioinformatics approaches for the study of molecular sex differences in complex diseases. It highlights that, beyond classical statistical methods, approaches are needed that integrate prior knowledge of relevant hormone signaling interactions, gene regulatory networks, and sex linkage of genes to provide a mechanistic interpretation of sex-dependent alterations in disease. The review examines and compares the advantages, pitfalls and limitations of various conventional statistical and systems-level mechanistic analyses for this purpose, including tailored pathway and network analysis techniques. Overall, this survey highlights the potential of specialized bioinformatics techniques to systematically investigate molecular sex differences in complex diseases, to inform biomarker signature modeling, and to guide more personalized treatment approaches.

Constraints on light dark sector particles from lifetime difference of heavy neutral mesons

Heavy meson decays with missing energy in the final state offer interesting avenues to search for light invisible new physics such as dark matter (DM). In this context, we show that such new physics (NP) interactions also affect lifetime difference in neutral meson-antimeson mixing. We consider general dimension-six effective quark interactions involving a pair of DM particles and calculate their contributions to lifetime difference in beauty and charm meson systems. We use the latest data on mixing observables to constrain the relevant effective operators. We find that lifetime differences provide novel and complementary flavor constraints compared to those obtained from heavy meson decays. Published by the American Physical Society 2024

Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff–Sagnotti counter-terms, and geometric flows

Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.