Conformal Theory Research Articles

Quantization of Carrollian conformal scalar theories

In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional (2D) magnetic scalar and three-dimensional (3D) electric and magnetic scalars. We discuss two different quantization schemes, depending on the choice of the vacuum. We show that the standard canonical quantization corresponding to the induced vacuum yields a unitary Hilbert space and the 2-point correlation functions in this scheme match exactly with the ones computed from the path integral. In the canonical quantization, the BMS symmetry can be realized without anomaly. On the other hand, for the quantization based on the highest-weight vacuum, it does not have a unitary Hilbert space. In 2D, the correlators in the highest-weight vacuum agree with the ones obtained by taking the c→0 limit of the 2D CFT, and there is an anomalous term in the commutation relations between the Virasoso generators, whose form is similar to the one in 2D CFT. In 3D, there is no good definition of the highest-weight vacuum without breaking the rotational symmetry. In our study, we find that the usual state-operator correspondence in CFT does not hold in the Carrollian case. Published by the American Physical Society 2024

Geometric Features of a Multivalent Function Pertaining to Fractional Operators

The Prabhakar fractional operator is commonly acclaimed as the queen model of fractional calculus. The distinction between univalent and multivalent functions became more formalized as part of the broader field of geometric function theory. This area of mathematics focuses on the study of analytic functions with specific geometric properties, such as injectivity, and their applications in various domains, including conformal mapping and potential theory. This paper’s goal is to discover new results of the harmonic multivalent functions defined in the open unit disc . Let present , the class of multivalent harmonic functions of the form in the open unit disc. Analyzing convolution with prabhahar fractional differential operator with multivalent harmonic function to be in the class . The coefficient inequality, growth rates, distortion properties, closure characteristics, neighborhood behaviors, and extreme points, all pertinent to this class were explored.

Constructing and Analyzing BiHom-(Pre-)Poisson Conformal Algebras

This study introduces the notions of BiHom-Poisson conformal algebra, BiHom-pre-Poisson conformal algebra, and their related structures. We show that many new BiHom-Poisson conformal algebras can be constructed from a BiHom-Poisson conformal algebra. In particular, the direct product of two BiHom-Poisson conformal algebras is also a BiHom-Poisson conformal algebra. We further describe the conformal bimodule and representation theory of the BiHom-Poisson conformal algebra. In addition, we define BiHom-pre-Poisson conformal algebra as the combination of BiHom-pre-Lie conformal algebra and BiHom-dendriform conformal algebra under some compatibility conditions. We further demonstrate a way to construct BiHom-Poisson conformal algebra from BiHom-pre-Poisson conformal algebra and provide the representation theory for BiHom-pre-Poisson conformal algebra. Finally, a detailed description of O-operators and Rota–Baxter operators on BiHom-Poisson conformal algebra is provided.

Holographic Gubser flow. A combined analytic and numerical study

Gubser flow is an evolution with cylindrical and boost symmetries, which can be best studied by mapping the future wedge of Minkowski space (R3,1) to dS3 × ℝ in a conformal relativistic theory. Here, we sharpen our previous analytic results and validate them via the first numerical exploration of the Gubser flow in a holographic conformal field theory.Remarkably, the leading generic behavior at large de Sitter time is free-streaming in transverse directions and the sub-leading behavior is that of a color glass condensate. We also show that Gubser flow can be smoothly glued to the vacuum outside the future Minkowski wedge generically given that the energy density vanishes faster than any power when extrapolated to early proper time or to large distances from the central axis. We find that at intermediate times the ratio of both the transverse and longitudinal pressures to the energy density converge approximately to a fixed point which is hydrodynamic only for large initial energy densities. We argue that our results suggest that the Gubser flow is better applied to collective behavior in jets rather than the full medium in the phenomenology of heavy ion collisions and can reveal new clues to the mechanism of confinement.

Wave metrics in the Cotton and conformal Killing gravity theories

Wave metrics in the Cotton and conformal Killing gravity theories

The Gauche‐Effect in 1,2‐Bis(arylsulfonate)ethanes

AbstractWith an aim of obtaining a fundamental understanding of C−C bond conformation theory, the molecular structure of an ethane with electron‐withdrawing groups, 1,2‐bis(4‐methoxybenzene‐sulfonate)ethane, was elucidated. According to the general conformation rule for alkanes, which states that molecules adopt a stabilized structure to avoid steric repulsion, ethanes typically adopt anti‐conformation. However, the title compound exhibited gauche‐conformation, as revealed by a single crystal diffraction study. Theoretical studies also support this behavior. Natural Bond Orbital (NBO) analysis suggests that the orbital interaction between the σ*CO orbital, attributable to the sulfonate groups, and the adjacent σCH orbital stabilizes the gauche‐conformation. The authors conclude that the sulfonate group acts as a gauche‐effect synthon, which is widely applicable in organic chemistry.

A Study on Chinese Translation of English-Japanese Movie Titles from the Perspective of Linguistic Conformity Theory

Movie translation plays an important role in the dissemination of a movie, just like the trademark and promotion card of a movie. It not only needs to match the style of the original movie, but also needs to have commercial value. The quality of title translation directly affects the box office and audience attendance. This paper takes the 250 movies with the highest Douban ratings as the research object, and collects relevant data by constructing a database. Through the literature survey, it is found that the current Chinese translation of movie title translation is mostly studied from the perspective of Purpose Theory and Dynamic Equivalence Theory, but a systematic framework has not yet been formed, so it is difficult to solve the problem of actual title translation. The purpose of this paper is to analyze the current problems in movie translation from the perspective of linguistic conformity theory, including copying and reproducing, formatting translation, unclear meaning, and words deviating from the theme. This paper argues that the proposed title translation should truly and accurately reflect the core of the original title and more deeply combine with the local culture, with the intention of providing new perspectives for movie translation to improve the translation quality of Chinese titles.

Confining strings in three-dimensional gauge theories beyond the Nambu-Gotō approximation

We carry out a systematic study of the effective bosonic string describing confining flux tubes in SU(N) Yang-Mills theories in three spacetime dimensions. While their low-energy properties are known to be universal and are described well by the Nambu-Gotō action, a non-trivial dependence on the gauge group is encoded in a series of undetermined subleading corrections in an expansion around the limit of an arbitrarily long string. We quantify the first two of these corrections by means of high-precision Monte Carlo simulations of Polyakov-loop correlators in the lattice regularization. We compare the results of novel lattice simulations for theories with N = 3 and 6 color charges, and report an improved estimate for the N = 2 case, discussing the approach to the large-N limit. Our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. In addition, we also present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions, finding that the lattice results for the Polyakov-loop correlation function are in excellent agreement with the predictions of the Svetitsky-Yaffe mapping, which are worked out quantitatively applying conformal perturbation theory to the three-state Potts model in two dimensions. The implications of these results are discussed.

Waves and strings in an interacting conformal chiral 2-form theory in six dimensions

In six dimensions there exists a unique one-parameter family of nonlinear conformal electrodynamics for a chiral 2-form gauge field that includes (in a free-field limit) the linear chiral 2-form theory and is related, by dimensional reduction, to the four-dimensional ModMax electrodynamics. In this work, we present the first exact solutions of this theory in presence of gravity. In particular, we will consider plane wave, Robinson-Trautman, and self-dual dyonic string configurations, generalizing well-known solutions of this type in six-dimensional supergravities with linear chiral 2-form multiplets. Published by the American Physical Society 2024

Geodesic conformal gradient device based on a torus.

In recent years, optical fields on non-Euclidean geometry have become a hot topic. The geodesic conformal transformation theory, linking curved surfaces with planar gradient refractive indices, holds unique advantages in controlling curved optical fields. However, this theory has not yet addressed surfaces with non-trivial topology with a certain genus. In this work, we design a gradient planar device based on the geodesic conformal transformation theory for toroidal surfaces, which can achieve Gaussian beam focusing. Unlike traditional angle-preserving geodesic theories, the non-zero genus results in the one-to-two discontinuous boundaries in the device, and we utilize inversion transformations to rectify this drawback.

Scale and conformal invariance on (A)dS spacetimes

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension D>4, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In D=4, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in D=4, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action. Published by the American Physical Society 2024

Reflected entropy and timelike entanglement in TT¯ -deformed CFT2s

We develop a covariant formalism to investigate the mixed state entanglement between time-dependent boosted subsystems in TT¯-deformed CFT2s through the reflected entropy. To this end we utilize a conformal perturbation theory to obtain the Rényi reflected entropy through the partition function on the replica manifold. The correction to the reflected entropy to the first order in the deformation parameter μ is then obtained in the replica limit for finite temperature and finite-sized systems. We further perform an analytic continuation of our results to obtain the reflected entropy for timelike subsystems in such TT¯-deformed CFT2s. We verify our field theoretic computations for both spacelike and timelike subsystems by obtaining the dual EWCS in the corresponding bulk cutoff AdS3 geometries and find perfect agreement between the two. Published by the American Physical Society 2024

The Difference Between the Theory of Conformity and Neo-Confucianism in the View of Truth

In philosophical theory, the understanding of "truth" can be divided into axiological truth and epistemological truth. The truth in the axiological sense mainly involves the problem of meaning and value, while the truth in the epistemological sense involves the problem of the conformity between the subject of knowledge and the object of knowledge or the objective reality. From the epistemological point of view, we can clarify the difference between the coincidence theory and the Chinese Neo-Confucianism in the view of truth so that we can not only explain the truth of each theory but also understand the harmonious relationship between the two views of truth.

First-order formalism for β functions in bosonic sigma models from supersymmetry breaking

We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional “geometric” results obtained in the background field methods, in this way resolving the peculiarities pointed out in O. Gamayun [Peculiarities of beta functions in sigma models, ]. The result is achieved by the supersymmetric completion of the first-order sigma model. Published by the American Physical Society 2024

Higgs branch of heterotic little string theories: Hasse diagrams and generalized symmetries

We study the Higgs branches of the 6D (1, 0) little string theories that live on the world volume of NS5-branes probing an ADE-singularity in the heterotic E8×E8 and Spin(32)/Z2 string theories. On the E8×E8 side, such little string theories (LSTs) are obtained via fusion of orbi-instanton SCFTs. For the C2/ZK orbifolds, we determine a magnetic quiver for the Higgs branch from the alternative type IIA brane system engineering the LST; we show that the magnetic quiver obtained in this way is the same as the Coulomb gauging of the 3D mirrors associated with the orbi-instanton building blocks. Using quiver subtraction, we determine the Hasse diagram of Higgs branch renormalization group flows between the LSTs, and we analyze how the structure constants of the generalized global symmetries vary along the edges of the Hasse diagram. From the Hasse diagram of the Higgs branch, we are immediately able to identify LSTs with the same T-duality-invariant properties, and thus propose candidate T-dual pairs. We perform a similar analysis of the Higgs branch Hasse diagram and putative T-dual families for particular E6-orbifold LSTs by taking advantage of a duality between a rank zero orbi-instanton theory and a rank one conformal matter theory. Published by the American Physical Society 2024

Vibration analysis of the propulsion shaft system considering dynamic misalignment in the outer ring

Propulsion shaft systems play a crucial role in marine applications, particularly in ships and underwater vehicles. However, existing research often overlooks the dynamics involved in the transmission of vibrations from the bearing to the housing and subsequently to the hull, which affects vibration control in marine equipment. Therefore, this study introduces an enhanced dynamic model for a propulsion shaft system, incorporating the dynamics of the bearing outer ring and housing. The proposed model deduces the deformation relationships between the ball and the inner/outer ring, considering the outer ring translation and swing. The contact force between the outer ring and bearing housing is calculated using conformal contact theory. Timoshenko beam theory is used to develop the shaft dynamic model, while the propeller, bearing components, and bearing housing are represented through the lumped parameter method. To validate the proposed model, an experiment is conducted, demonstrating its accuracy. The study provides analysis of the bearing contact force, shaft dynamics, and bearing housing dynamics. Additionally, the influence of bearing clearances on the shaft and bearing housing dynamics is investigated. The results show that controlling bearing #2 clearance to below 20 μm helps reduce the system vibrations.

Deconfined quantum criticality of nodal d -wave superconductivity, Néel order, and charge order on the square lattice at half-filling

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the π-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background π-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal d-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases that are very likely described by (2+1)-dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional d-wave superconductor with gapless Bogoliubov quasiparticles at four nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semimetal phases. Published by the American Physical Society 2024

Fusion and Positivity in Chiral Conformal Field Theory

In this article we show that the conformal nets corresponding to WZW models are rational, resolving a long-standing open problem. Specifically, we show that the Jones-Wassermann subfactors associated with these models have finite index. This result was first conjectured in the early 90s but had previously only been proven in special cases, beginning with Wassermann’s landmark results in type A. The proof relies on a new framework for the systematic comparison of tensor products (a.k.a. ‘fusion’) of conformal net representations with the corresponding tensor product of vertex operator algebra modules. This framework is based on the geometric technique of ‘bounded localized vertex operators,’ which realizes algebras of observables via insertion operators localized in partially thin Riemann surfaces. We obtain a general method for showing that Jones-Wassermann subfactors have finite index, and apply it to additional families of important examples beyond WZW models. We also consider applications to a class of positivity phenomena for VOAs, and use this to outline a program for identifying unitary tensor product theories of VOAs and conformal nets even for badly-behaved models.

Alzheimer's disease diagnosis by applying Shannon entropy to Ricci flow-based surface indexing and extreme gradient boosting

Geometric surface models are extensively utilized in brain imaging to analyze and compare three-dimensional anatomical shapes. Due to the intricate nature of the brain surface, rather than examining the entire cortical surface, we are introducing a new set of signatures focused on characteristics of the hippocampal region, which is linked to aspects of Alzheimer's disease. Our approach focuses on Ricci flow as a conformal parameterization method, permitting us to calculate the conformal factor and mean curvature as conformal surface representations to identify distinct regions within a three-dimensional mesh. For the first time for such settings, we propose a simple while elegant formulation by employing the well-established concept of Shannon entropy on these well-known features. This compact while rich feature formulation turns out to lead to an efficient local surface encoding. We are validating its effectiveness through a series of preliminary experiments on 3D MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), with the aim of diagnosing Alzheimer's disease. The feature vectors generated and inputted into the XGBoost classifier demonstrate a remarkable level of accuracy, further emphasizing their potential as a valuable additional measure for surface-based cortical morphometry in Alzheimer's disease research.

Conformal perturbation theory for n-point functions: structure constant deformation

We consider conformal perturbation theory for n-point functions on the sphere in general 2D CFTs to first order in coupling constant. We regulate perturbation integrals using canonical hard disk excisions of size ϵ around the fixed operator insertions, and identify the full set of counter terms which are sufficient to regulate all such integrated n-point functions. We further explore the integrated 4-point function which computes changes to the structure constants of the theory. Using an sl(2) map, the three fixed locations of operators are mapped to 0, 1, and ∞. We show that approximating the mapped excised regions to leading order in ϵ does not lead to the same perturbative shift to the structure constant as the exact in ϵ region. We explicitly compute the correction back to the exact in ϵ region of integration in terms of the CFT data. We consider the compact boson, and show that one must use the exact in ϵ region to obtain agreement with the exact results for structure constants in this theory.