Search Results (126)

Conformal field theory is quantized on the ideal boundary of a Riemann surface, and the effect on the widths of the resonances of the quantum states is evaluated. The resonances on a surface can be recast in terms of eigenfunctions of a differential operator on the Mandelstam plane. Cusps in this plane, representing Landau singularities, reflect a divergence in the coupling. A cusp on the Riemann surface similarly causes a divergence in the scattering amplitude. The interpretation of the string diagram indicates that the self-interaction of the string in the vicinity of the cusp causes it to implode, which would require an infinite coupling. A consistent physical interpretation of cusps on surfaces requires supersymmetry. The study of unitary minimal models and N = 2 superminimal models indicates that there can exist a set of resonances at the cusps and ends of the surfaces. The uncertainty in the masses of six types of particles at a finite set of cusps is infinitesimal. Tachyon condensation on the ideal boundary would introduce an uncertainty in the mass of a charged particle. The widths of charged particle resonances at the ends of infinite-genus surfaces is not negligible and can be traced to the coupling with tachyons. Full article

We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the n-ary sigma matrices defined in earlier work. In this way, polyadic analogs of supercharges and Hamiltonians take the cyclic shift block matrix form, and they are different from the N-extended and multigraded SQM. While constructing the corresponding supersymmetry as an n-ary Lie superalgebra (n is the arity of the initial associative multiplication), we have found new brackets with a reduced arity of $2\le m<n$ and a related series of m-ary superalgebras (which is impossible for binary superalgebras). In the case of even reduced arity m, we obtain a tower of higher-order (as differential operators) even Hamiltonians, while for m odd we obtain a tower of higher-order odd supercharges, and the corresponding algebra consists of the odd sector only. Full article

As shown by Dyson in his famous paper “Missed Opportunities”, it follows, even from purely mathematical considerations, that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Thus, the usual explanation of why, in particle physics, Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts, while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators $M_{4\mu }$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{\mu \nu }$ ($\mu ,\nu =0,1,2,3$). We explicitly show that this is the case in the Flato–Fronsdal approach, where elementary particles in standard theory are bound states of two Dirac singletons. Full article

We propose a distinct mechanism to explain the matter–antimatter imbalance observed in the universe, rooted in quantum entanglement asymmetry (QEA). Our concept of QEA differs from its usage in the recent literature, where it typically measures how much symmetry is broken within a subsystem of a larger quantum system. Here, we define QEA as an intrinsic asymmetry in the entanglement properties of particle–antiparticle pairs in the early universe, leading to a preferential survival of matter over antimatter. We develop a theoretical framework incorporating QEA into the standard cosmological model, providing clear justification for the asymmetry in entangled states and corresponding modifications to the Hamiltonian. Numerical simulations using lattice Quantum Chromodynamics (QCD) demonstrate that QEA can produce a net baryon asymmetry consistent with observations. We also predict specific signatures in Cosmic Microwave Background (CMB) anisotropies and large-scale structure formation, offering potential avenues for empirical verification. This work aims to deepen the understanding of cosmological asymmetries and highlight the significance of quantum entanglement in the universe’s evolution. Full article

We study an interesting superization problem of integrable nonlinear dynamical systems on functional manifolds. As an example, we considered a quantum many-particle Schrödinger–Davydov model on the axis, whose quasi-classical reduction proved to be a completely integrable Hamiltonian system on a smooth functional manifold. We checked that the so-called “naive” approach, based on the superization of the related phase space variables via extending the corresponding Poisson brackets upon the related functional supermanifold, fails to retain the dynamical system super-integrability. Moreover, we demonstrated that there exists a wide class of classical Lax-type integrable nonlinear dynamical systems on axes in relation to which a superization scheme consists in a reasonable superization of the related Lax-type representation by means of passing from the basic algebra of pseudo-differential operators on the axis to the corresponding superalgebra of super-pseudodifferential operators on the superaxis. Full article

This review begins with the standard Lie symmetry theory for nonlinear PDEs and explores extensions of symmetry analysis. First, it introduces three key symmetry reduction methods: the classical symmetry method, conditional symmetries, and the CK direct method. Next, it presents two finite symmetry transformation group methods—one related to Lax pairs and one independent of them. The fourth section reviews four nonlocal symmetry methods based on conserved forms, conformal invariants, Darboux transformations, and Lax pairs. The final section covers supersymmetry theory and supersymmetric dark equations. Each method is illustrated with examples and references. Full article

We successively reanalyzed modern Lie-algebraic approaches lying in the background of effective constructions of integrable super-Hamiltonian systems on functional $N=1,2,3$- supermanifolds, possessing rich supersymmetries and endowed with suitably related compatible Poisson structures. As an application, we describe countable hierarchies of new nonlinear Lax-type integrable $N=2,3$-semi-supersymmetric dynamical systems and constructed their central extended superconformal Lie superalgebra $\mathcal{K}(1|3)$ and its finite-dimensional coadjoint orbits, generated by the related Casimir functionals. Moreover, we generalized these results subject to the suitably factorized super-pseudo-differential Lax-type representations and present the related super-Poisson brackets and compatible suitably factorized Hamiltonian superflows. As an interesting point, we succeeded in the algorithmic construction of integrable super-Hamiltonian factorized systems generated by Casimir invariants of the centrally extended super-pseudo-differential operator Lie superalgebras on the $N=1,2,3$-supercircle. Full article

This article is a shortened review of previous results obtained by the author. The advantages of describing the geometric nature of the physical properties of the early universe using the Clifford algebra approach are demonstrated. A geometric representation of the wave function of the early universe is used, and a new mechanism of spontaneous symmetry breaking with different degrees of freedom is proposed. A possible supersymmetry is revealed, and it is shown that the energy of the initial vacuum can be considered equal to zero. The origin of baryonic asymmetry and the nature of dark matter can be explained using a geometric representation of the wave function of the early universe. Full article

Natural supersymmetry with light higgsinos is most favored to emerge from the string landscape, since the volume of a scan parameter space shrinks to tiny volumes for electroweak unnatural models. Rather general arguments favor a landscape selection of soft SUSY breaking terms tilted to large values, but they are tempered by the atomic principle that the derived value of the weak scale in each pocket universe lies not too far from its measured value in our universe. But, that leaves (at least) three different paradigms for gaugino masses in natural SUSY models: unified (as in nonuniversal Higgs models), anomaly mediation form (as in natural AMSB), and mirage mediation form (with comparable moduli- and anomaly-mediated contributions). We perform landscape scans for each of these, and we show that they populate different, but overlapping, positions in $m(\mathit{\ell }\overline{\ell })$ and $m\left(wino\right)$ space. The first of these may be directly measurable at high-lumi LHC via the soft opposite-sign dilepton plus jets plus $E{/}_T$ signature arising from higgsino pair production, while the second of these could be extracted from direct wino pair production, leading to same-sign diboson production. Full article

In flipped SU(5) grand unified theories, the partial decay lifetimes of certain nucleon decay channels depend generically on an unknown unitary matrix, which arises when left-handed lepton fields are embedded into anti-fundamental representations of SU(5). This dependency is particularly relevant when the neutrino mass matrix has a generic structure, introducing uncertainty in the prediction of nucleon decay branching fractions within flipped SU(5). In this paper, we demonstrate that this uncertainty can be parametrized using two parameters, which can be determined by measuring the partial lifetimes of $p\to {\pi }^0{e}^{+}$, $p\to {\pi }^0{\mu }^{+}$, and $n\to {\pi }^0\overline{\nu }$. In addition, we establish upper limits on the ratios of the decay widths of these channels, offering a potential method to test flipped SU(5) in future nucleon decay experiments. Full article

Until now, research has not taken into consideration the physicochemical purine–pyrimidine symmetries of the genetic code in the transcription and translation processes of proteinogenesis. Our Supersymmetry Genetic Code table, developed in 2022, is common and unique for all RNA and DNA living species. Its basic structure is a purine–pyrimidine symmetry net with double mirror symmetry. Accordingly, the symmetry of the genetic code directly shows its organisation based on the principle of nucleotide Watson–Crick and codon–anticodon pairing. The maximal purine–pyrimidine symmetries of codons show that each codon has a strictly defined and unchangeable position within the genetic code. We discovered that the physicochemical symmetries of the genetic code play a fundamental role in recognising and differentiating codons from mRNA and the anticodon tRNA and aminoacyl-tRNA synthetases in the transcription and translation processes. These symmetries also support the wobble hypothesis with non-Watson–Crick pairing interactions between the translation process from mRNA to tRNA. The Supersymmetry Genetic Code table shows a specific arrangement of the second base of codons, according to which it is possible that an anticodon from tRNA recognises whether a codon from mRNA belongs to an amino acid with two or four codons, which is very important in the purposeful use of the wobble pairing process. Therefore, we show that canonical and wobble pairings essentially do not lead to misreading and errors during translation, and we point out the role of physicochemical purine–pyrimidine symmetries in decreasing disorder according to error minimisation and preserving the integrity of biological processes during proteinogenesis. Full article

The paper reveals some remarkable form-invariance features of the ‘Jacobi-reference’ canonical Sturm–Liouville equation (CSLE) in the particular case of the density function with the simple pole at the origin. It is proven that the CSLE under consideration preserves its form under the two second-order Darboux–Crum transformations (DCTs) with the seed functions represented by specially chosen pairs of ‘basic’ quasi-rational solutions (q-RSs), i.e., such that their analytical continuations do not have zeros in the complex plane. It is proven that both transformations generally either increase or decrease by 2 the exponent difference (ExpDiff) for the mentioned pole while keeping two other parameters unchanged. The change is more complicated in the latter case if the ExpDiff for the pole of the original CSLE at the origin is smaller than 2. It was observed that the DCTs in question do not preserve bound energy levels according to the conventional supersymmetry (SUSY) rules. To understand this anomaly, we split the DCT in question into the two sequential Darboux deformations of the Liouville potentials associated with the CSLEs of our interest. We found that the first Darboux transformation turns the initial CSLE into the Heun equation written in the canonical form while the second transformation brings us back to the canonical form of the hypergeometric equation. It is shown that the first of these transformations necessarily places the mentioned ExpDiff into the limit-circle (LC) range and then the second transformation keeps the pole within the LC region, violating the conventional prescriptions of SUSY quantum mechanics. Full article

Because there are a few typos in the supersymmetry-breaking sfermion masses and trilinear soft term, regarding the current Large Hadron Collider (LHC) and dark matter searches, we revisit a three-family Pati–Salam model based on intersecting D6-branes in Type IIA string theory on a ${\mathbf{T}}^{\mathbf{6}}/({\mathbb{Z}}_{\mathbf{2}}\times {\mathbb{Z}}_{\mathbf{2}})$ orientifold with a realistic phenomenology. We study the viable parameter space and discuss the spectrum consistent with the current LHC Supersymmetry searches and the dark matter relic density bounds from the Planck 2018 data. For the gluinos and first two generations of sfermions, we observe that the gluino mass is in the range [2, 14] TeV, the squarks mass range is [2, 13] TeV and the sleptons mass is in the range [1, 5] TeV. We achieve the cold dark matter relic density consistent with 5$\sigma$ Planck 2018 bounds via A-funnel and coannihilation channels such as stop–neutralino, stau–neutralino, and chargino–neutralino. Except for a few chargino–neutralino coannihilation solutions, these solutions satisfy current nucleon-neutralino spin-independent and spin-dependent scattering cross-sections and may be probed by future dark matter searches. Full article

Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different $4-d$ laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological constant, it may also predict the form of weak scale supersymmetry which is expected to emerge. Rather general arguments suggest a power-law draw to large soft terms, but these are subject to an anthropic selection of a not-too-large value for the weak scale. The combined selection allows one to compute relative probabilities for the emergence of supersymmetric models from the landscape. Models with weak scale naturalness appear most likely to emerge since they have the largest parameter space on the landscape. For finetuned models such as high-scale SUSY or split SUSY, the required weak scale finetuning shrinks their parameter space to tiny volumes, making them much less likely to appear compared to natural models. Probability distributions for sparticle and Higgs masses from natural models show a preference for Higgs mass $m_h\sim 125$ GeV, with sparticles typically beyond the present LHC limits, in accord with data. From these considerations, we briefly describe how natural SUSY is expected to be revealed at future LHC upgrades. This article is a contribution to the Special Edition of the journal Entropy, honoring Paul Frampton on his 80th birthday. Full article

In this study, we once again use a set of Fibonacci-like sequences to examine the symmetries within the genetic code. This time, our focus is on the physiological state of the amino acids, considering them as charged, in contrast to our previous work where they were seen as neutral. In a pH environment around 7.4, there are four charged amino acids. We utilize the properties of our sequences to accurately describe the symmetries in the genetic code table. These include Rumer’s symmetry, the third-base symmetry and the “ideal” symmetry, along with the “supersymmetry” classification schemes. We also explore the special chemical structure of the amino acid proline, presenting two perspectives—shCherbak’s view and the Downes–Richardson view—which are included in the description of the above-mentioned symmetries. Our investigation also employs elementary modular arithmetic to precisely describe the chemical structure of proline, connecting the two views seamlessly. Finally, our Fibonacci-like sequences prove instrumental in quickly establishing the multiplet structure of non-standard versions of the genetic code. We illustrate this with an example, showcasing the efficiency of our method in unraveling the complex relationships within the genetic code. Full article