Conformal Structure Research Articles

Charting the conformal manifold of holographic CFT$_2$'s

We construct new continuous families of AdS_3× S^3× T^4AdS3×S3×T4 and AdS_3× S^3× S^3× S^1AdS3×S3×S3×S1 solutions in heterotic and type II supergravities. These families are found in three-dimensional consistent truncations and controlled by 17 parameters, which include TsT \betaβ deformations and encompass several supersymmetric sub-families. The different uplifts are constructed in a unified fashion by means of Exceptional Field Theory (ExFT). This allows the computation of the Kaluza-Klein spectra around the deformations, to test the stability of the solutions, and to interpret them holographically and as worldsheet models. To achieve this, we describe how the half-maximal S(8,8)S(8,8) ExFT can be embedded into E_{8(8)}E8(8) ExFT.

Self-dual cosmology

We construct cosmological spacetimes with a self-dual Weyl tensor whose dynamics are described by conformally coupled scalars with only cubic self-interactions. Similar to the previously discovered cases in flat and (Anti) de Sitter backgrounds, the interactions are characterized by a bracket that encodes a kinematic algebra. We discuss how the color-kinematics duality and double copy are realized in these cosmological backgrounds. If we further impose that the Ricci scalar is that of an FLRW spacetime, we find two new self-dual metrics corresponding to radiation-dominated and coasting (non-accelerating) FLRW backgrounds. Relaxing this requirement, we find an infinite family of solutions given by three different conformal classes of cosmological self-dual metrics. These solutions approximate those of FLRW as long as we impose a simple additional constraint on the scalar theory.

Galilean fluids from non-relativistic gravity

The 1/c-expansion of general relativity appropriately sourced by matter can be used to derive an action principle for Newtonian gravity. The gravitational part of this action is known as non-relativistic gravity (NRG). It is possible to source NRG differently and in such a way that one can construct solutions that are not described by Newtonian gravity (as they do not admit a notion of absolute time). It is possible to include a negative cosmological constant such that NRG admits a non-relativistic AdS solution. This non-relativistic AdS vacuum has Killing vectors that form the Galilean conformal algebra and a boundary that admits a conformal class of Newton-Cartan geometries. This begs the question of whether there exists an analogue of the fluid/gravity correspondence for NRG. In this paper we derive a non-relativistic AdS brane solution of NRG and confirm that it corresponds to the 1/c2-expansion of the AdS black brane geometry. We perform a Galilean boost of the non-relativistic AdS brane and derive the associated boundary energy-momentum tensor. We then show that this is the energy-momentum tensor of a massless Galilean fluid and explain how this is linked to the conformal isometries of the boundary. Along the way, we also present several new results for the theory of non-relativistic gravity itself. In particular we present a rewriting that greatly shortens and simplifies the equations of motion of the NRG action.

Blackening S-folds

We construct the universal AdS4 black hole that asymptotes to the (φ, χ)-family of type IIB S-fold backgrounds dual to the conformal manifold of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 S-fold CFT’s. We present the explicit type IIB embedding of such a universal black hole for two particular asymptotics: the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 S-fold with U(2) symmetry at (φ, χ) = (0, 0) and the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 S-fold with SO(4) symmetry at (φ, χ) = (1, 0). As a byproduct, we also present a novel two-parameter family of AdS2 × M8 supersymmetric S-fold backgrounds with M8 = ℍ2 × S5 × S1 that features a parametrically-controlled scale separation involving some of the internal directions.

Dirac Eigenvalue Optimisation and Harmonic Maps to Complex Projective Spaces

Abstract Consider a Dirac operator on an oriented compact surface endowed with a Riemannian metric and spin structure. Provided the area and the conformal class are fixed, how small can the $k$-th positive Dirac eigenvalue be? This problem mirrors the maximization problem for the eigenvalues of the Laplacian, which is related to the study of harmonic maps into spheres. We uncover the connection between the critical metrics for Dirac eigenvalues and harmonic maps into complex projective spaces. Using this approach we show that for many conformal classes on a torus the first nonzero Dirac eigenvalue is minimised by the flat metric. We also present a new geometric proof of Bär’s theorem stating that the first nonzero Dirac eigenvalue on the sphere is minimised by the standard round metric.

The Effects of Mechanical Loading on Resonant Response of a Conformal Load-Bearing Antenna System.

Glass fibre-reinforced polymer (GFRP) is a suitable substrate material for constructing a Conformal Load-Bearing Antenna Structure (CLAS). The relative permittivity of the CLAS substrate, which determines its resonant frequency, is affected by damage sustained by GFRP. This paper investigates the effects of damage (induced by mechanically loading the substrate) on the resonant response of the CLAS. Decoupling the antenna from the substrate was essential to evaluate the CLAS's true response to the induced damage. This paper details a systematic investigation examining how the frequency response of a "pristine" antenna and a surface-mounted antenna respond to a substrate subjected to quasi-statically induced mechanical damage and cyclic fatigue loading. The results demonstrate that the resonant frequency of the CLAS varies as a function of the substrate's mechanical damage. The prepared CLAS is tolerant to a certain degree of mechanical loading and related damage with its resonant frequency remaining within an acceptable bandwidth.

Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations

A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds the existence of an essential conformal transformation forces the manifold to be conformally flat. This is false for pseudo-Riemannian manifolds, however compact examples of conformally curved manifolds with essential conformal transformation are scarce. Here we give examples of compact conformal manifolds in signature $(4n+2k,4n+2\ell)$ with essential conformal transformations that are locally conformally pseudo-Kähler and not conformally flat, where $n\ge 1$, $k, \ell \ge 0$. The corresponding local pseudo-Kähler metrics obtained by a local conformal rescaling are Ricci-flat.

Flexible Tactile Sensors with Gradient Conformal Dome Structures.

The trade-off between high sensitivity and wide detection range remains a challenge for flexible capacitive pressure sensors. Gradient structure can provide continuous deformation and lead to a wide sensing range. However, it simultaneously augments the distance between two electrodes, which diminishes the variation in the relative distance and results in a decreased sensitivity. Herein, a conformal design is introduced into the gradient structure to construct a flexible capacitive pressure sensor. The gradient conformal dome structure is fabricated by a simple reverse dome adsorption process. Taking advantage of the progressive deformation behavior of the gradient dielectric, and the significant improvement of relative distance variation between two electrodes from the conformal design, the sensor achieves a sensitivity of 0.214 kPa-1 in an ultrabroad linear range up to 200 kPa. It maintains high-pressure resolution under the preload of 10 and 100 kPa. Benefiting from the rapid response and excellent repeatability, the sensor can be used for physiological monitor and human motion detection, including arterial pulse, joint bending, and motion state. The gradient conformal design strategy may pave a promising avenue to develop pressure sensors with high sensitivity and wide linear range.

Conformal structure of singularities in some varying fundamental constants bimetric cosmologies

In this paper, we explore the conformal structure of singularities arising from varying fundamental constants using the method of Penrose diagrams. We employ a specific type of bimetric model featuring two different metrics. One metric describes the causal structure for matter, while the other characterizes the causal structure for gravitational interactions, which is related to variations in fundamental constants such as the gravitational constant and the speed of light. For this reason, we focused on the gravitational metric to calculate the conformal transformation and compose Penrose diagrams for the singularities arising from the varying fundamental constants. We have shown that, in one case, the parameter such as the scale factor, the density and the pressure resemble those of the finite scale factor singularity (FSF). Despite singularity appears in constant conformal time in our case and in the case of FSF the Misner-Sharp horizon looks different. Our another case is similar to sudden future singularity (SFS), but there are differences in the conformal structures. We have also shown that in our cases the behavior of Misner-Sharp horizon strongly depends on initial conditions. The last analytical solution which we introduced is identical to conformal structure of the standard exotic singularity for the matter.

MOF-Derived Ni/NiO-C Nanocomposites as Bifunctional Electrocatalysts Capable of Driving Both ORR and OER.

Bifunctional electrocatalysts, capable of efficiently driving both the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER), are crucial for advancing electrochemical processes. While noble-metal-based catalysts are widely recognized for their role in oxygen processes, current state-of-the-art designs are limited to either ORR or OER activity, presenting a notable research gap. In addressing this challenge, we have developed a novel Ni/NiO-C nanocomposite catalyst derived from a nickel-based metal-organic framework (Ni-SKU-5). For the ORR, the Ni/NiO-C catalyst exhibits an onset potential of 0.95 V vs RHE in a 1.0 M KOH solution, coupled with a Tafel slope of -99 mV dec-1 at 1600 rpm. Moreover, the catalyst displays excellent stability, maintaining a performance of over 90% after 10 h of continuous reaction. Furthermore, the catalyst proves effective in the OER, boasting an overpotential of 370 mV (at 10 mA cm-2) and a Tafel slope of 114 mV dec-1, highlighting its bifunctionality. The bifunctional overpotential of the Ni/NiO-C composite is measured at 820 mV, surpassing that of the 20% Pt/C electrocatalyst (860 mV), highlighting its potential for practical applications. Comparative experiments establish the origin of the robust bifunctional reactivity toward the conformal hybrid structure, porous framework, and the synergistic effect operating among the constituents of the nanocomposite.

Deformational rigidity of integrable metrics on the torus

Abstract It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: we consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations, the deformed metric is again Liouville. The principal idea of the argument is that the preservation of rational invariant tori in the foliation of the phase space forces a linear combination on the Fourier coefficients of the deformation to vanish. Showing that the resulting linear system is non-degenerate will then yield the claim. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. To put our results in perspective, we review existing results about integrable metrics on the torus.

The gap phenomenon for conformally related Einstein metrics

AbstractWe determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension of the conformally nonflat conformal manifold. In definite signature, these two dimensions are at most and , respectively. In Lorentzian signature, these two dimensions are at most and , respectively. In the remaining signatures, these two dimensions are at most and , respectively. This upper bound is sharp and to realize examples of submaximal dimensions, we first provide them directly in dimension 4. In higher dimensions, we construct the submaximal examples as the (warped) product of the (pseudo)‐Euclidean base of dimension with one of the 4‐dimensional submaximal examples.

Fixed lines in four fermion models in two dimensions

Motivated by conjectures about near-horizon dynamics in quantum gravity, we search for lines of perturbatively accessible fixed points emanating from models of N free fermions. Through two loops we find a new class of models, apart from the well-known Abelian Thirring models. Further study is needed to see whether these can lead to true conformal manifolds, or perhaps a new class of large-N fixed points. Published by the American Physical Society 2024

Cosmological observatories

Abstract We study the static patch of de Sitter space in the presence of a timelike boundary. We impose that the conformal class of the induced metric and the trace of the extrinsic curvature, K, are fixed at the boundary. We present the thermodynamic structure of de Sitter space subject to these boundary conditions, for static and spherically symmetric configurations to leading order in the semiclassical approximation. In three spacetime dimensions, and taking K constant on a toroidal Euclidean boundary, we find that the spacetime is thermally stable for all K. In four spacetime dimensions, the thermal stability depends on the value of K. It is established that for sufficiently large K, the de Sitter static patch subject to conformal boundary conditions is thermally stable. This contrasts the Dirichlet problem for which the region encompassing the cosmological horizon has negative specific heat. We present an analysis of the linearised Einstein equations subject to conformal boundary conditions. In the worldline limit of the timelike boundary, the underlying modes are linked to the quasinormal modes of the static patch. In the limit where the timelike boundary approaches the cosmological event horizon, the linearised modes are interpreted in terms of the shear and sound modes of a fluid dynamical system. Additionally, we find modes with a frequency of positive imaginary part. Measured in a local inertial reference frame, and taking the stretched cosmological horizon limit, these modes grow at most polynomially.

Malfunctioning conformal phased array: Radiation pattern recovery with particle swarm optimisation

AbstractThe electronic beam steering in conformal phased arrays is formed by exciting the multiple antennas with appropriate phase shifts. However, the malfunctioning of phase shifters connected to the central antenna elements in the conformal array distorts the radiation pattern of the array system severely as compared to edge elements resulting in the reduction of the array gain and increase in the side lobe levels. Here, the authors propose a non‐dominated sorting multi‐objective particle swarm optimisation (NS‐MOPSO) technique capable of recalculating the independent phases of working antenna elements in the array in such a manner as to correct the overall radiation pattern. To illustrate the radiation pattern's recovery capabilities of the optimisation technique in case of malfunctioning of any random phase shifter(s), a 1 x 7 microstrip patch antenna array operating at 2.45 GHz on a wedge‐shaped conformal structure was designed in CST simulator. To test, the radiation pattern's recovery capabilities of the NS‐MOPSO approach, phase shifters connected to the antenna elements in the array were made to malfunction. Then the optimisation algorithm recalculates the phases for individual antenna elements to achieve the desired corrected radiation pattern. The simulated and measured radiation pattern recovery results are in good agreement with each other.

Ising meson spectroscopy on a noisy digital quantum simulator

Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

On the geometry of semi-slant submanifolds of a conformal Kenmotsu manifold

Abstract The object of this paper is to conduct an in-depth examination of semi-slant submanifolds within the framework of a conformal Kenmotsu manifolds. Our investigation is centered around identifying and understanding the conditions that ensure the integrability of both invariant and slant distributions, which play a pivotal role in defining semi-slant submanifolds. Additionally, we prove some interesting results for semi-slant submanifolds with parallel canonical structures.

Asymptotic symmetries of gravity in the gauge PDE approach

We propose a framework to study local gauge theories on manifolds with boundaries and their asymptotic symmetries, which is based on representing them as so-called gauge PDEs. These objects extend the conventional BV-AKSZ sigma-models to the case of not necessarily topological and diffeomorphism invariant systems and are known to behave well when restricted to submanifolds and boundaries. We introduce the notion of gauge PDE with boundaries, which takes into account generic boundary conditions, and apply the framework to asymptotically flat gravity. In so doing, we start with a suitable representation of gravity as a gauge PDE with boundaries, which implements the Penrose description of asymptotically simple spacetimes. We then derive the minimal model of the gauge PDE induced on the boundary and observe that it provides the Cartan (frame-like) description of a (curved) conformal Carollian structure on the boundary. Furthermore, imposing a version of the familiar boundary conditions in the induced boundary gauge PDE, leads immediately to the conventional Bondi–Metzner–Sachs algebra of asymptotic symmetries. Finally, we briefly sketch the construction for asymptotically (A)dS gravity.

Competitive Intramolecular Hydrogen Bonding: Offering Molecules a Choice.

The conformational preferences of N-((6-methylpyridin-2-yl)carbamothioyl)benzamide were studied in solution, the gas phase and the solid state via a combination of NMR, density functional theory (DFT) and single crystal X-ray techniques. This acyl thiourea derivative can adopt two classes of low energy conformation, each stabilized by a different 6-membered intramolecular hydrogen bond (IHB) pseudoring. Analysis in different solvents revealed that the conformational preference of this molecule is polarity dependent, with increasingly polar environments yielding a higher proportion of the minor conformer containing an NH⋅⋅⋅N IHB. The calculated barrier to interconversion is consistent with dynamic behaviour at room temperature, despite the propensity of 6-membered IHB pseudorings to be static. This work demonstrates that introducing competitive IHB pathways can render static IHBs more dynamic and that such systems could have potential as chameleons in drug design.

Green synthesis of N, B co-doped TiO2 nanoparticles with enhanced photocatalytic and antioxidant activities

BackgroundReactive dyes are widely used in the fabric production, and because they are poisonous, and hazardous, their release into the environment today indicates a rise in pollution in the environment. Biosynthetic approach that is also environmentally benign has gained an abundance of recognition for its eco-friendly products, biocompatibility, and long-term economic viability. MethodsIn the present investigation, TiO2 (T) and N, B co-doped-TiO2 (NB-T) nanoparticles (NPs) were prepared biologically using mangrove aqueous extract by the sol-gel method to compare their photocatalytic degradation activity of an aqueous solution of reactive red 250 dye (RR250) under visible light irradiation at different times. The antioxidant activities of T and NB-T NPs samples were evaluated. The synthesized samples were characterized using different techniques. Main findingsThe findings showed that photocatalytic degradation activity of NB-T NPs reaches 100 % after 60 min of the degradation process, where it reaches maximum (38.1 %) for T NPs at the highest catalyst dose. The results showed that NB-T NPs have a conformal surface structure and stronger photocatalytic properties than Pure T. Measurements of Chemical Oxygen Demand (COD) were made, and a significant reduction in values was seen, showing the technique's high potential for removing RR250 dye from aqueous solutions. The NB-T sample showed the maximum activity, as indicated by the estimated IC50 value (34.98 μg/mL). Both T and NB-T NPs showed significant DPPH free radical scavenging activity.