We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the <math><mrow><mi>SU</mi></mrow><mo>(</mo><mi>n</mi><mo>)</mo></math> hyper-Kähler quotient (HKQ) of the Coulomb branch of a 3d <math><mi>N</mi><mo>=</mo><mn>4</mn></math> unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as “good” or “ugly”, which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are “bad”, differing thereby from quiver subtractions based on Kraft-Procesi transitions. The simple diagrammatic procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.

United Kingdom

Quotient quiver subtraction

Given an associative ring of <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math>-graded operators, the number of inequivalent brackets of Lie-type which are compatible with the grading and satisfy graded Jacobi identities is <math><msub><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mi>n</mi><mo>+</mo><mo>⌊</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo>⌋</mo><mo>+</mo><mn>1</mn></math>. This follows from the Rittenberg-Wyler and Scheunert analysis of “color” Lie (super)algebras which is revisited here in terms of Boolean logic gates.The inequivalent brackets, recovered from <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>×</mo><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mo>→</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> mappings, are defined by consistent sets of commutators/anticommutators describing particles accommodated into an n-bit parastatistics (ordinary bosons/fermions correspond to 1 bit). Depending on the given graded Lie (super)algebra, its graded sectors can fall into different classes of equivalence expressing different types of particles (bosons, parabosons, fermions, parafermions). As a consequence, the assignment of certain “marked” operators to a given graded sector is a further mechanism to induce inequivalent graded Lie (super)algebras (the basic examples of quaternions, split-quaternions and biquaternions illustrate these features).As a first application we construct <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math> and <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msubsup></math>-graded quantum Hamiltonians which respectively admit <math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>4</mn></math> and <math><msub><mrow><mi>b</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>=</mo><mn>5</mn></math> inequivalent multiparticle quantizations (the inequivalent parastatistics are discriminated by measuring the eigenvalues of certain observables in some given states). The extension to <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math>-graded quantum Hamiltonians for <math><mi>n</mi><mo>&gt;</mo><mn>3</mn></math> is immediate.As a main physical application we prove that the <math><mi>N</mi></math>-extended, one-dimensional supersymmetric and superconformal quantum mechanics, for <math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn></math>, are respectively described by <math><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>14</mn></math> alternative formulations based on the inequivalent graded Lie (super)algebras. The <math><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi></mrow></msub></math> numbers correspond to all possible “statistical transmutations” of a given set of supercharges which, for <math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>8</mn></math>, are accommodated into a <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math>-grading with <math><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math> (the identification is <math><mi>N</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math>).In the simplest <math><mi>N</mi><mo>=</mo><mn>2</mn></math> setting (the 2-particle sector of the de Alfaro-Fubini-Furlan deformed oscillator with <math><mi>s</mi><mi>l</mi><mo>(</mo><mn>2</mn><mo>|</mo><mn>1</mn><mo>)</mo></math> spectrum-generating superalgebra), the <math><msubsup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math>-graded parastatistics imply a degeneration of the energy levels which cannot be reproduced by ordinary bosons/fermions statistics.

Brazil

Inequivalent -graded Brackets, -bit Parastatistics and Statistical Transmutations of Supersymmetric Quantum Mechanics

In this paper, we have studied the effects of holographic dark energy on the evolution of gravitational waves. The background evolution of gravitational waves in a flat FRW universe is considered and studied in the presence of various holographic dark energy models. The perturbation equations governing the evolution of the gravitational waves have been constructed and solutions are obtained. These solutions are studied in detail to get a proper understanding of the characteristics of the gravitational waves in the presence of holographic dark energy. The work can be a significant tool in studying different dark energy models comparatively using the features of the gravitational wave evolution.

India

Gravitational waves driven by holographic dark energy

This paper presents the CMB angular power spectrum obtained using the CAMB code for three different models of inflation: the Starobinsky inflationary model, the generalized Starobinsky inflationary model, and the chaotic inflationary model with a step. The results are compared with the most recent data reported for the Planck mission. An analysis of the large (<math><mi>ℓ</mi><mo>≲</mo><mn>90</mn></math>), intermediate (<math><mn>90</mn><mo>≲</mo><mi>ℓ</mi><mo>≲</mo><mn>900</mn></math>), and small (<math><mi>ℓ</mi><mo>≳</mo><mn>900</mn></math>) angular scales is performed. We report the position of the peaks in the intermediate region so as the cosmological parameters obtained in each of the models: age of the universe, <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>m</mi></mrow></msub></math>, <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>b</mi></mrow></msub></math>, <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>Λ</mi></mrow></msub></math>, <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>K</mi></mrow></msub></math> and <math><msub><mrow><mi>n</mi></mrow><mrow><mi>S</mi></mrow></msub></math>. We also perform a Bayesian analysis using the Cobaya code to evaluate our three best-fitting models. Additionally, we generated contour plots <math><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mi>S</mi></mrow></msub><mo>,</mo><mi>r</mi><mo>)</mo></math> for our inflationary models, taking into account the number of e–folds between the end of inflation and the completion of reheating.

Ecuador

Mexico

Observational predictions of some inflationary models

We study the <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> gravity in the framework of Weyl geometry (known as Weyl-type <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> gravity), where Q denotes the non-metricity scalar, and T denotes the energy-momentum tensor trace. In this work, we consider the <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> model, which is defined as <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>α</mi><msup><mrow><mi>Q</mi></mrow><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mfrac><mrow><mi>β</mi></mrow><mrow><mn>6</mn><msup><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mi>T</mi></math> and investigating two scenarios: (I) <math><mi>m</mi><mo>=</mo><mn>0</mn></math> (linear model) and <math><mo>(</mo><mi>I</mi><mi>I</mi><mo>)</mo></math> <math><mi>m</mi><mo>≠</mo><mn>0</mn></math> (nonlinear model). For both scenarios, we find the explicit solution for the field equations by using the barotropic equation of state as <math><mi>p</mi><mo>=</mo><mi>w</mi><mi>ρ</mi></math>, where w is the equation-of-state (EoS) parameter. Further, we study the obtained solutions statistically using the <math><mi>P</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>o</mi><msup><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msup></math> (Without SHOES Calibrated) dataset with 1701 data points. For both models, the best-fit values of model parameters for <math><mn>1</mn><mo>−</mo><mi>σ</mi></math> and <math><mn>2</mn><mo>−</mo><mi>σ</mi></math> confidence level. The higher Hubble constant values in both models emphasize the presence of Tension. We statistically compare our models to the ΛCDM model using <math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math>, <math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>r</mi><mi>e</mi><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math>, AIC, <math><mi>Δ</mi><mi>A</mi><mi>I</mi><mi>C</mi></math>, BIC and <math><mi>Δ</mi><mi>B</mi><mi>I</mi><mi>C</mi></math>. We also examine cosmological parameters such as deceleration and EoS parameters to determine the current acceleration expansion of the Universe. Furthermore, we test our model using Om diagnostic and compare it to the ΛCDM model to determine its dark energy profile. Finally, we draw the conclusion that statistically speaking, both linear and nonlinear models show good compatibility with the ΛCDM model.

Romania

Azerbaijan

Morocco

Statistical and observation comparison of Weyl-type ( , ) models with the ΛCDM paradigm

We develop formulations for barrow holographic dark energy (BHDE) in both non-interacting and interacting scenarios within a cosmological framework, applying the conventional holographic principle. Model parameter constraints are determined through the Markov Chain Monte Carlo (MCMC) method, utilizing different datasets. The investigation excavates into the models' kinematic behavior, exploring the transition from deceleration to acceleration and tracking the evolution of the equation of state parameters. Further, these models can pretend the evolution of dark energy and matter in the Universe. Additionally, a thermodynamic analysis employing future event horizons is conducted, confirming the validation of the generalized second law of thermodynamics. The resultant of the BHDE models strongly suggests that the Universe is presently experiencing an accelerated phase attributed to dark energy.

Probing barrow entropy models with future event horizon as IR cutoff

We propose an extended 2HDM with <math><msub><mrow><mi>Q</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>×</mo><msub><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msub></math> symmetry that can successfully accommodate the SM fermion mass and mixing hierarchy. The tiny masses of the active neutrinos are generated from a type-I seesaw mechanism mediated by very heavy right-handed Majorana neutrinos. The model gives a natural explanation of the charged lepton mass hierarchy. Besides that, the experimental values of the physical observables of the neutrino sector: the neutrino mass squared splittings, the leptonic mixing angles and the leptonic Dirac CP violating phase, are also successfully reproduced for both normal and inverted neutrino mass hierarchies. We find a feasible range of values for the leptonic Dirac CP phase to be in the ranges <math><msub><mrow><mi>δ</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>∈</mo><msup><mrow><mo>(</mo><mn>305.90</mn><mo>,</mo><mn>348.70</mn><mo>)</mo></mrow><mrow><mo>∘</mo></mrow></msup></math> for normal ordering and <math><msub><mrow><mi>δ</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo>∈</mo><msup><mrow><mo>(</mo><mn>308.00</mn><mo>,</mo><mn>348.00</mn><mo>)</mo></mrow><mrow><mo>∘</mo></mrow></msup></math> for inverted ordering, which is consistent with the 3σ experimentally allowed limits. The sum of neutrino masses is obtained as <math><mo>∑</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mo>(</mo><mn>58.03</mn><mo>,</mo><mn>60.51</mn><mo>)</mo></math> meV for normal ordering and <math><mo>∑</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mo>(</mo><mn>98.07</mn><mo>,</mo><mn>101.40</mn><mo>)</mo></math> meV for inverted ordering which are well consistent with all the recent limits. In addition, the obtained ranges for the effective neutrino masses are <math><mo>〈</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>〉</mo><mo>∈</mo><mo>(</mo><mn>3.80</mn><mo>,</mo><mn>4.38</mn><mo>)</mo></math> meV, <math><msub><mrow><mi>m</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>∈</mo><mo>(</mo><mn>8.53</mn><mo>,</mo><mn>9.34</mn><mo>)</mo><mspace width="0.25em"></mspace><mtext>meV</mtext></math> for normal ordering and <math><mo>〈</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub><mo>〉</mo><mo>∈</mo><mo>(</mo><mn>47.85</mn><mo>,</mo><mn>49.58</mn><mo>)</mo></math> meV, <math><msub><mrow><mi>m</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>∈</mo><mo>(</mo><mn>48.39</mn><mo>,</mo><mn>50.09</mn><mo>)</mo><mspace width="0.25em"></mspace><mtext>meV</mtext></math> for inverted ordering which are in agreement with the recent experimental bounds. For the quark sector, the derived results are also in agreement with the recent data on the quark masses and mixing angles. The model under consideration can also accommodate the muon anomalous magnetic moment.

Vietnam

Chile

Fermion masses and mixings and − 2 Muon Anomaly in a flavored 2HDM

The EW-<math><msub><mrow><mi>ν</mi></mrow><mrow><mi>R</mi></mrow></msub></math> model was constructed in order to provide a seesaw scenario operating at the Electroweak scale <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>E</mi><mi>W</mi></mrow></msub><mo>∼</mo><mn>246</mn></math> GeV, keeping the same SM gauge structure. In this model, right-handed neutrinos are non-sterile and have masses of the order <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>E</mi><mi>W</mi></mrow></msub></math>. They can be searched for at the LHC along with heavy mirror quarks and leptons, the lightest of which has large decay lengths. The model also incorporates a rich scalar sector, consistent with various experimental constraints, predicts a ∼125 GeV scalar with the SM Higgs characteristics satisfying the current LHC Higgs boson data. The seesaw mechanism requires the existence of a complex scalar which is singlet under the SM gauge group. The imaginary part of this complex scalar denoted by <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math> is proposed to be the sub-MeV dark matter candidate in this manuscript. We find that the sub-MeV scalar can serve as a viable non-thermal feebly interacting massive particle (FIMP)-DM candidate. This <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math> can be a naturally light sub-MeV DM candidate due to its nature as a pseudo-Nambu-Goldstone (PNG) boson in the model. We show that the well-studied freeze out mechanism falls short in this particular framework producing DM overabundance. We identify that the freeze in mechanism produces the correct order of relic density for the sub-MeV DM candidate satisfying all applicable constraints. We also discuss the allowed parameter space arising from the current indirect search bounds for this sub-MeV DM.

United States

A model of light pseudoscalar dark matter

The Casas-Ibarra (CI) parametrization of the Yukawa coupling matrix of Majorana neutrinos is generalized by considering the exact seesaw relation and including non-unitarity of the <math><mn>3</mn><mo>×</mo><mn>3</mn></math> Pontecorvo-Maki-Nakagawa-Sakata (PMNS) flavor mixing matrix. With the help of a full <math><mn>6</mn><mo>×</mo><mn>6</mn></math> Euler-like block description of the flavor structure for the seesaw mechanism, we find that the orthogonal matrix <math><mi>O</mi></math> in the CI parametrization can be expressed as <math><msub><mrow><mi>O</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><msqrt><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msqrt><mspace width="0.05cm"></mspace><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> with <math><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub></math> and <math><msub><mrow><mi>M</mi></mrow><mrow><mi>j</mi></mrow></msub></math> being the masses of light and heavy Majorana neutrinos and <math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math> consisting of the PMNS and active-sterile flavor mixing parameters (for <math><mi>i</mi><mo>,</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></math>). Assuming a specific pattern of <math><mi>O</mi></math> is therefore equivalent to imposing some special conditions on the seesaw parameter space.

China

On the orthogonal matrix in the Casas-Ibarra parametrization for the Yukawa interactions of Majorana neutrinos

We perform an analysis of the consequences of various new physics operators on the lepton flavor violating (LFV) decay modes mediated through <math><mi>b</mi><mo>→</mo><mi>s</mi><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math> transitions. We scrutinize the imprints of the (pseudo)scalar and axial (vector) operators on the exclusive LFV decay channels <math><msub><mrow><mi>B</mi></mrow><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow></msub><mo>→</mo><mo>(</mo><mi>ϕ</mi><mo>,</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>)</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><mi>Λ</mi><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math>, where <math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math> represent μ or τ. The new physics parameters are constrained by using the upper limits of the branching fractions of the <math><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>→</mo><mi>τ</mi><mi>μ</mi></math> and <math><mi>B</mi><mo>→</mo><mi>K</mi><mi>τ</mi><mi>μ</mi></math> processes, assuming the new physics couplings to be real. We then explore the key observables such as the branching fractions, the forward-backward asymmetries, and the longitudinal polarization fractions of the <math><mi>B</mi><mo>→</mo><mo>(</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><mi>ϕ</mi><mo>,</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>)</mo><msup><mrow><mi>τ</mi></mrow><mrow><mo>±</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>∓</mo></mrow></msup></math> decays. In addition, we also investigate the impact of the new physics couplings on the baryonic <math><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><mi>Λ</mi><msup><mrow><mi>τ</mi></mrow><mrow><mo>±</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>∓</mo></mrow></msup></math> decay channels mediated by the <math><mi>b</mi><mo>→</mo><mi>s</mi></math> quark level transition. With the experimental prospects at LHCb upgrade and Belle II, we also predict the upper limits of the above-discussed observables, which could intrigue the new physics search in these channels.