Conformal Theory Research Articles

Integrable Z 2 2-graded extensions of the Liouville and Sinh-Gordon theories

Abstract In this paper we present a general framework to construct integrable Z 2 2-graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and Sinh-Gordon models; they are based on Z 2 2-graded color Lie algebras and their fields satisfy a parabosonic statististics. The mathematical tools here introduced are the Z 2 2-graded covariant extensions of the Lax pair formalism and of the Polyakov's soldering procedure. The Z 2 2-graded Sinh-Gordon model is derived from an affine Z 2 2-graded color Lie algebra, mimicking a procedure originally introduced by Babelon-Bonora to derive the ordinary Sinh-Gordon model. The color Lie algebras under considerations are: the 6-generator Z 2 2-graded sl2, the Z 2 2-graded affine ${\widehat{sl_2}}$ algebra with two central extensions, the Z 2 2-graded Virasoro algebra obtained from a Hamiltonian reduction.

Holographic Renyi entropy of 2d CFT in KdV generalized ensemble

The eigenstate thermalization hypothesis (ETH) in chaotic two dimensional CFTs is subtle due to infinitely many conserved KdV charges. Previous works have demonstrated that primary CFT eigenstates have flat entanglement spectrum, which is very different from the microcanonical ensemble. This result is an apparent contradiction to conventional ETH, which does not take KdV charges into account. In a companion paper [1], we resolve this discrepancy by studying the subsystem entropy of a chaotic CFT in KdV-generalized Gibbs and microcanonical ensembles. In this paper, we carry out parallel computations in the context of AdS/CFT. We focus on the high density limit, which is equivalent to thermodynamic limit in conformal theories. In this limit holographic Renyi entropy can be computed using the so-called gluing construction. We explicitly study the KdV-generalized microcanonical ensemble with the densities of the first two KdV charges Q1 = q1, Q3 = q3 fixed and obeying q3−q12≪q12. In this regime we found that the refined Renyi entropy S~n is n-independent for n > ncut, where ncut depends on q1, q3. By taking the primary state limit q3 → q12, we recover flat entanglement spectrum characteristic of fixed-area states, in agreement with the primary state behavior. This provides a consistency check of the KdV-generalized ETH in 2d CFTs.

Non-invertible symmetry in Calabi-Yau conformal field theories

We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. By deforming away from this special locus using exactly marginal operators, we then identify submanifolds in moduli space where some non-invertible symmetry persists. For instance, along ten-dimensional loci in the complex structure moduli space of quintic Calabi-Yau threefolds there is a symmetry characterized by a Fibonacci fusion category. The symmetries we identify provide new constraints on spectra and correlation functions. As an application we show how they constrain conformal perturbation theory, consistent with recent results about scaling dimensions in the K3 sigma model near its Gepner point.

Unravelling AdS3/CFT2 near the boundary

We study correlation functions of spectrally-flowed vertex operators in bosonic string theory on AdS3 × \U0001d44b in the path integral formalism. By restricting the path integral to only include worldsheets which live near the asymptotic boundary, we compute correlation functions of spectrally-flowed vertex operators and find a precise agreement with the perturbative correlators in the recently-proposed dual CFT at all orders in conformal perturbation theory. We thus provide highly nontrivial evidence for the bulk/boundary duality.

Prestressed and prepolarized piezoelectric material with an elliptical hole

In this paper, the antiplane state problem of an elliptic hole in a prestressed and prepolarized piezoelectric material loaded by constant, uniform remote shear stresses was performed. A compact and elementary form solution of the problem is obtained utilizing the conformal mapping technique and representation of the incremental stress and electrical fields by complex potentials. Using the boundary conditions, the coefficients of complex potentials developed as Laurent series, for the case of a piezoelectric material of class 4¯2m, and implicitly the components of incremental stress and electric displacement fields are obtained in a final compact and closed form.

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

Integrated correlators in a N = 2 SYM theory with fundamental flavors: a matrix-model perspective

The D theory is a N = 2 conformal SYM theory in four dimensions with gauge group SU(N), four matter hypermultiplets in the fundamental and two in the anti-symmetric representation, and a flavor symmetry that contains a U(4) factor. Its holographic dual is obtained via a combination of orbifold and orientifold projections from Type II B string theory on AdS5 × S5 and possesses a sector of open strings attached to D7 branes with U(4) Chan-Paton factors. The AdS Veneziano amplitude of the U(4) gluons is dual to four-point correlators of moment-map operators of the U(4) flavor symmetry in the D theory. An integrated version of these correlators is captured by a deformation of the D theory in which the fundamental hypermultiplets acquire a mass. The partition function of this massive theory can be evaluated with matrix-model techniques using localization. In this paper we analyze the matrix model of the mass-deformed D theory arising from localization using the so-called “full Lie algebra” approach in a 1/N expansion. In particular, we study the partition function and its mass derivatives up to O(1/N2) corrections obtaining exact expressions that are valid for all values of the ’t Hooft coupling. We also analyze their behavior at strong coupling where our results produce useful constraints on the dual open string scattering amplitudes in AdS.

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