Conformal Group Research Articles

A Scalar Product for Computing Fundamental Quantities in Matter

We introduce a systematic way to obtain expressions for computing the amount of fundamental quantities such as helicity and angular momentum contained in static matter, given its charge and magnetization densities. The method is based on a scalar product that we put forward which is invariant under the ten-parameter conformal group in three-dimensional Euclidean space. This group is obtained as the static restriction (frequency ω=0) of the symmetry group of Maxwell equations: The fifteen-parameter conformal group in 3+1 Minkowski spacetime. In an exemplary application, we compute the helicity and angular momentum squared stored in a magnetic Hopfion.

A constructive solution to the cosmological bootstrap

In this paper we revisit a generalised crossing equation that follows from harmonic analysis on the conformal group, and is of particular interest for the cosmological bootstrap programme. We present an exact solution to this equation, for dimensions two or higher, in terms of 6j symbols of the Euclidean conformal group, and discuss its relevance. In the process we provide a detailed derivation of the analogue of the Biedenharn-Elliot identity for said 6j symbols.

Multi-scale alignment in highly piezoelectric polyacrylonitrile nanofibers separator for advanced self-charging supercapacitor

Self-charging supercapacitor (SCSPC) is an integrated device that can convert mechanical energy into electrical energy and store it to power microelectronics without need a rectifier for DC conversion. Here, we report a multi-alignment design idea for polyacrylonitrile (PAN) piezoelectric nanofiber instead of traditional polyvinylidene fluoride (PVDF) as a separator in SCSPCs, which greatly improves device self-charging performance and index. The combination of synergistic effect of polarization and the stretching process in electrospinning technology can achieve PAN nanofibers orderly arrangement at macroscopic level and alignment of conformation and cyano groups at microstructural level, resulting in excellent hydrophilicity (contact angle 0 °), high piezoelectric property (3.80 μW at a load resistance of 1 MΩ), high mechanical property (7.77 MPa), and outstanding cycling stability (unchanged after 22,000 cycles). As a result, the SCSPCs based on PAN piezoelectric separator has a high conversion efficiency of 12.53%, an energy density of 37.60 mJ cm−2 at power density of 1.01 mW cm−2, and a capacitance retention 91.7% after 5000 compressive cycles. The SCSPC@PAN with working area of 4 × 4 cm2 was attached on elbow, shoes, and bicycle tire to collect biomechanical energy and covert mechanical energy into electrical energy and store. Two SCSPC@PAN in series attached on one shoe can light 3.0 V LEDs after working for 40 min. This multi-scale alignment design idea and understanding the relationship between structure of PAN piezoelectric membrane and properties of SCSPC@PAN would provide important basis for design advanced piezoelectric separator for SCSPCs.

Separate Gut Plasma Cell Populations Produce Auto-Antibodies against Transglutaminase 2 and Transglutaminase 3 in Dermatitis Herpetiformis.

Dermatitis herpetiformis (DH) is an inflammatory skin disorder often considered as an extra intestinal manifestation of celiac disease (CeD). Hallmarks of CeD and DH are auto-antibodies to transglutaminase 2 (TG2) and transglutaminase 3 (TG3), respectively. DH patients have auto-antibodies reactive with both transglutaminase enzymes. Here it is reported that in DH both gut plasma cells and serum auto-antibodies are specific for either TG2 or TG3 with no TG2-TG3 cross reactivity. By generating monoclonal antibodies from TG3-specific duodenal plasma cells of DH patients, three conformational epitope groups are defined. Both TG2-specific and TG3-specific gut plasma cells have few immunoglobulin (Ig) mutations, and the two transglutaminase-reactive populations show distinct selection of certain heavy and light chain V-genes. Mass spectrometry analysis of TG3-specific serum IgA corroborates preferential usage of IGHV2-5 in combination with IGKV4-1. Collectively, these results demonstrate parallel induction of anti-TG2 and anti-TG3 auto-antibody responses involving separate B-cell populations in DH patients.

Ehlers, Carroll, charges and dual charges

We unravel the boundary manifestation of Ehlers’ hidden Möbius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry and are Petrov-algebraic. This is achieved in a designated gauge, shaped in the spirit of flat holography, where the Carrollian three-dimensional nature of the null conformal boundary is manifest and covariantly implemented. The action of the Möbius group is local on the space of Carrollian boundary data, among which the Carrollian Cotton tensor plays a predominent role. The Carrollian and Weyl geometric tools introduced for shaping an appropriate gauge, as well as the boundary conformal group, which is BMS4, allow to define electric/magnetic, leading/subleading towers of charges directly from the boundary Carrollian dynamics and explore their behaviour under the action of the Möbius duality group.

Chemometric approaches as an effective way to study conformer populations of lidocaine molecules in supercritical carbon dioxide

In this work, we studied the equilibrium between lidocaine conformers with an intramolecular hydrogen bond and those without such bond in a diluted lidocaine solution in scCO2 (with the lidocaine concentration of ∼10–2 mol/l) in the pressure range of 100–300 bar at the temperature of 35 °C. We conducted a comprehensive study of the spectral band related to the stretching vibrations of the N–H fragment of the lidocaine molecule. We applied a combination of chemometric approaches including principal component analysis and two-dimensional correlation spectroscopy along with traditional analysis of the ν(N–H) band.Based on the obtained results we found that there are three groups of lidocaine conformers in the studied solution. According to the quantum chemical calculations performed, we attributed two of the groups to the conformers characterized by the presence of an intramolecular hydrogen bond and the third group was linked to the conformers without such bond. We discovered that over the whole pressure range studied, lidocaine conformers with an intramolecular hydrogen bond prevail in the solution. Additionally, we showed that although there is only a small population of conformers without an intramolecular hydrogen bond and this number remains constant in the pressure range studied, the existence of such conformers in the solution cannot be neglected due to their statistically valuable quantity.

Local Rigidity by Flexibility: Unusual Design for Organic THz‐Device Materials

AbstractTerahertz (THz) waves interact with molecular phonon vibrations of organic matter. When designing organic THz‐device materials, conformational flexible groups (CFGs) are in most cases avoided. CFGs create many low‐energy conformers with high conformational entropy, which results in large and many phonon vibration modes that lead to undesired self‐absorption of THz waves. Here, nonpolar CFGs only having weak intermolecular interaction capability are unusually introduced into organic THz‐device materials, utilized for efficient THz wave generation. Newly designed THz‐source crystals possess nonpolar methylene (CH2)n units having high conformational flexibility. Compared to previously reported benchmark crystals without methylene CFGs, introducing methylene CFGs significantly reduces void volume in newly designed crystals. This leads to the suppression of molecular phonon vibrations below 2.0 THz (i.e., introducing flexibility results in local rigidity). At infrared pump wavelengths, new CFG‐contained crystals generate a strong THz electric field that is one order of magnitude stronger than that generated in inorganic ZnTe crystals. CFG‐contained crystals exhibit a flatter spectral shape of the generated THz wave than benchmark crystals without methylene CFGs. Therefore, the introduction of CFGs is a very intriguing design strategy for organic THz‐device materials to reduce the limitations caused by phonon vibrations.

Remarks on higher Schwarzians

The Schwarzian derivative has recently received renewed attention in connection with the study of the Sachdev–Ye–Kitaev model. In mathematics literature, various higher order generalizations of the Schwarzian derivative are known due to Aharonov, Bertilsson, and Schippers. Physical applications of the higher Schwarzian derivatives have not yet been discussed in any detail. In this work, we link Bertilsson's variant to the ℓ–conformal Galilei group, as well as discuss some of its interesting peculiarities. These include a recurrence relation, which allows one to construct the higher Schwarzians iteratively, a composition law, and symmetry transformations.

Conformational State of Fenamates at the Membrane Interface: A MAS NOESY Study.

The present work analyzes the 1H NOESY MAS NMR spectra of three fenamates (mefenamic, tolfenamic, and flufenamic acids) localized in the lipid-water interface of phosphatidyloleoylphosphatidylcholine (POPC) membranes. The observed cross-peaks in the two-dimensional NMR spectra characterized intramolecular proximities between the hydrogen atoms of the fenamates as well as intermolecular interactions between the fenamates and POPC molecules. The peak amplitude normalization for an improved cross-relaxation (PANIC) approach, the isolated spin-pair approximation (ISPA) model, and the two-position exchange model were used to calculate the interproton distances indicative of specific conformations of the fenamates. The results showed that the proportions of the A+C and B+D conformer groups of mefenamic and tolfenamic acids in the presence of POPC were comparable within the experimental error and amounted to 47.8%/52.2% and 47.7%/52.3%, respectively. In contrast, these proportions for the flufenamic acid conformers differed and amounted to 56.6%/43.4%. This allowed us to conclude that when they bind to the POPC model lipid membrane, fenamate molecules change their conformational equilibria.

Modular Hamiltonian of the scalar in the semi infinite line: dimensional reduction for spherically symmetric regions

We focus our attention on the one dimensional scalar theories that result from dimensionally reducing the free scalar field theory in arbitrary d dimensions. As is well known, after integrating out the angular coordinates, the free scalar theory can be expressed as an infinite sum of theories living in the semi-infinite line, labeled by the angular modes left{ell, overrightarrow{m}right} . We show that their modular Hamiltonian in an interval attached to the origin is, in turn, the one obtained from the dimensional reduction of the modular Hamiltonian of the conformal parent theory in a sphere. Remarkably, this is a local expression in the energy density, as happens in the conformal case, although the resulting one-dimensional theories are clearly not conformal. We support this result by analyzing the symmetries of these theories, which turn out to be a portion of the original conformal group, and proving that the reduced modular Hamiltonian is in fact the operator generating the modular flow in the interval. By studying the spectrum of these modular Hamiltonians, we also provide an analytic expression for the associated entanglement entropy. Finally, extending the radial regularization scheme originally introduced by Srednicki, we sum over the angular modes to successfully recover the conformal anomaly in the entropy logarithmic coefficient in even dimensions, as well as the universal constant F term in d = 3.

Probing holography in p -adic CFT

We holographically calculate the partition functions of certain types of isotropic sectors of the CFTs dual to Bruhat-Tits trees and $p$-adic BTZ black holes. Along the way, we propose new spectral decompositions of the Laplacian operator other than the plane-wave basis on these two types of background, with both analytical and numerical evidence. We extract the density of states and hence entropy from the BTZ partition function via the inverse Laplace transform. Then the one-loop Witten diagram is computed in the $p$-adic BTZ black hole background, yielding constraints on the heavy-heavy-light averaged three-point coefficient of its boundary $p$-adic CFT. Finally, for general $p$-adic CFTs (not necessarily holographic), we analyze the representation theory of their global conformal group $PGL\left(2,\mathbb{Q}_p\right)$, and discuss the suitability of different representations as Hilbert spaces of $p$-adic CFT.

Does DMSO affect the conformational changes of drug molecules in supercritical CO2 Media?

This work investigated the effect of DMSO‑d6 on the conformation of lidocaine and fenamates. Using lidocaine as a model compound, the study investigated the influence of DMSO‑d6 on the conformational preferences of fenamates, which have similar fragment structures to the molecule. The NOESY spectra of mefenamic, flufenamic and tolfenamic acid were compared in a mixture of scCO2 + DMSO‑d6 at the same state parameters as lidocaine (45 °C and 9 MPa). The two-position exchange model was used to calculate the proportions of fenamate conformer groups in scCO2 + DMSO‑d6. The addition of DMSO‑d6 did not significantly alter the conformation of mefenamic acid, and the ratio of conformers was determined to be 75.3 / 24.7, which is very close to the previously measured in pure scCO2. The results showed that the addition of DMSO‑d6 did not significantly alter the conformation of lidocaine and mefenamic acid. This suggests that adding 2 %, DMSO‑d6 can be used to evaluate the structure of poorly soluble drug compounds using the NOESY method in supercritical carbon dioxide. The findings of this study are encouraging.

Quantum Chiral Superfields

We define the ordinary Minkowski space inside the conformal space according to Penrose and Manin as homogeneous spaces for the Poincaré and conformal group respectively. We realize the supersymmetric (SUSY) generalizations of such homogeneous spaces over the complex and the real fields. We finally investigate chiral (antichiral) superfields, which are superfields on the super Grassmannian, Gr(2|1, 4|1), respectively on Gr(2|0, 4|1). They ultimately give the twistor coordinates necessary to describe the conformal superspace as the flag Fl(2|0, 2|1; 4|1) and the Minkowski superspace as its big cell.

Recent advances in the biological activities of microbial exopolysaccharides.

Microbial exopolysaccharides (EPSs) are valuable extracellular macromolecules secreted as capsules or slime layers. Various microorganisms, including bacteria, yeasts, fungi, and algae have been studied for their ability to produce EPSs. Microbial EPSs exist as homopolysaccharides or heteropolysaccharides with various properties such as different monosaccharide compositions, structural conformation, molecular weight, and functional groups. They are cost-effective alternatives to plant and animal-derived polysaccharides because the microbial cells produced them in large quantities by biotechnological processes using low-cost substrates such as industrial wastes in a short time. Microbial EPSs are safe, biodegradable, and compatible polymers. They have extensive bioactivities, including antibacterial, antifungal, antiviral, antioxidant, antitumor, antidiabetic, antiulcer, anticoagulant, antiaging, immunomodulatory, wound healing, and cholesterol-lowering activities. Microbial EPSs owing to biological activities, special biochemical structures, and attractive physicochemical properties find plenty of potential applications in various industries. The enhancement of the production of EPSs and improving their properties can be provided by genetic engineering methods. The current review aims to provide a comprehensive examination of the therapeutic activities of microbial EPSs in infectious diseases and metabolic disorders, with a focus on the mechanisms involved. Also, the effect of the physicochemical characteristics of EPSs on these bioactivities was discussed to reveal the structure-activity relationship.

The shadow formalism of Galilean CFT2

In this work, we develop the shadow formalism for two-dimensional Galilean conformal field theory (GCFT2). We define the principal series representation of Galilean conformal symmetry group and find its relation with the Wigner classification, then we determine the shadow transform of local operators. Using this formalism we derive the OPE blocks, Clebsch-Gordan kernels, conformal blocks and conformal partial waves. A new feature is that the conformal block admits additional branch points, which would destroy the convergence of OPE for certain parameters. We establish another inversion formula different from the previous one, but get the same result when decomposing the four-point functions in the mean field theory (MFT). We also construct a continuous series of bilocal actions of MFT, and an exceptional series of local actions, one of which is the BMS free scalar model. We notice that there is an outer automorphism of the Galilean conformal symmetry, and the GCFT2 can be regarded as null defect in higher dimensional CFTs.

Zooming in on the horizon when in its Meissner state

When approaching extremality, rotating black holes tend to expel the magnetic field in which they are immersed. This phenomenon, being reminiscent of the Meissner-Ochsenfeld effect in superconductors, is known as the black hole Meissner effect, and here we study it in the backreacting regime and from the near horizon perspective. By resorting to methods recently developed in the literature, which allow to compute conserved charges in the near horizon region, regardless the details of the asymptotia at large distance, we investigate the properties of the black hole horizon when in its Meissner state. We show that, when in such state, the horizon exhibits two sets of supertranslation symmetries as well as a symmetry generated by the local conformal group. The supertranslations are generated by two infinite sets of currents, one of which comes from local dilations of the advanced null coordinate at the horizon, and the other from local gauge transformations that preserve the electromagnetic field configuration at the horizon. We show that the evaluation of the conserved charges associated to these symmetries correctly reproduce the physical charges of the magnetized black holes and their thermodynamics. This represents a concrete application of the techniques developed in [1–3] and it extends the results of [4] to arbitrary values of the black hole charges. In addition, we elaborate on the charges computation at the horizon: we show the equivalence between the horizon charges and the evaluation of the corresponding Komar integrals. Besides, we show the validity of the Gauss phenomenon by explicitly relating near horizon charges with fluxes and charges computed by other techniques. All this provides a method to derive the thermodynamics of magnetized horizons in a quite succinct way, including the case of horizons exhibiting the Meissner effect.

Comparison of functional and oncological outcome of conformal sphincter preservation operation, low anterior resection, and abdominoperineal resection in very low rectal cancer: a retrospective comparative cohort study with propensity score matching.

Conformal sphincter preservation operation (CSPO) procedure is a sphincter preservation procedure for preserving the anal canal function for very low rectal cancers. This study investigated the functional and oncological outcome of conformal sphincter preservation operation by comparing with low anterior resection (LAR) and abdominoperineal resection (APR). This is a retrospective comparative study. Patients who received conformal sphincter preservation operation (n=52), low anterior resection (n=54), or abdominoperineal resection (n=69) were included between 2011 and 2016 in a tertiary referral hospital. Propensity score matching was applied to adjust the baseline characteristics which may influence the choice of the surgical procedure. Twenty-one pairs of conformal sphincter preservation operation vs. low anterior resection and 29 pairs of conformal sphincter preservation operation vs. abdominoperineal resection were selected. The first group had a higher tumor location than the second group. Compared with the low anterior resection group, the conformal sphincter preservation operation group had shorter distal resection margins; however, no significant differences were identified in daily stool frequency, Wexner incontinence score, local recurrence, distant metastasis, overall survival, and disease-free survival between both groups. Compared with the abdominoperineal resection group, the conformal sphincter preservation operation group had shorter operative time and shorter postoperative hospital stay. No significant differences were identified in local recurrence, distant metastasis, overall survival, and disease-free survival. Conformal sphincter preservation operation is oncologically safe compared to APR and LAR, and has similar functional findings to LAR. Studies comparing CSPO with intersphincteric resection should be performed.

Classical and quantum particles from nongeneric conformal orbits

The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary representations of conformal group fit into the classification described by Mack (1977) [31].

Proper extensions of the 2-sphere’s conformal group present entropy and are 4-transitive

AbstractIn this paper, we prove using elementary techniques that any group of diffeomorphisms acting on the 2-sphere and properly extending the conformal group of Möbius transformations must be at least 4-transitive or, more precisely, arc 4-transitive. As an important consequence, we derive that any such group must always contain an element of positive topological entropy. We also provide a self-contained characterization, in terms of transitivity, of the Möbius transformations within the full group of sphere diffeomorphisms.

Effect of physiological pH on the molecular characteristics, rheological behavior, and molecular dynamics of κ-carrageenan/casein.

During gastrointestinal digestion, κ-carrageenan (κ-CGN) undergoes physicochemical changes, which associated with the risk of colitis. To understand the effect of physiological pH on the conformational transition and binding stability of κ-CGN and κ-carrageenan/casein (κ-CC), we conducted experiments at pH 3.0 (gastric environment) and pH 7.0 (intestinal environment). We evaluated zeta potential, free sulfate group content, Fourier transform infrared spectroscopy, thermodynamic properties, microstructure, and molecular mechanism. Our results revealed that the helical conformation of κ-CGN and κ-CC were more ordered and stable, and sulfate group exposure both lower in the intestinal environment (pH 7.0). However, in gastric environment (pH 3.0), the charge density of κ-CGN decreased, accompanied by random curling conformation and free sulfate group content increased. In contrast, the intermolecular interactions between κ-CGN and casein increased in gastric acid environments due to casein flocculation and secondary structure folding, and significantly reduced the exposure of free sulfate groups of κ-CGN. Our research results provide an important theoretical basis for elucidating the molecular mechanism and structure-activity relationship of κ-CGN under casein matrix to protect the mucosal barrier and inhibit colitis, and are of great significance for guiding and expanding the safe application of κ-CGN, thus assisting food nutrition to be absorbed.