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In this paper, we construct the super Virasoro algebra with an arbitrary conformal dimension $\mathrm{\Delta }$ from the generalized ${ℛ}(p,q)$-deformed quantum algebra and investigate the ${ℛ}(p,q)$-deformed super Virasoro algebra with the particular conformal dimension $\mathrm{\Delta }=1.$ Furthermore, we perform the ${ℛ}(p,q)$-conformal Virasoro $n$-algebra, the ${ℛ}(p,q)$-conformal super Virasoro $n$-algebra ($n$-even) and discuss a toy model for the ${ℛ}(p,q)$-conformal Virasoro constraints and ${ℛ}(p,q)$-conformal super Virasoro constraints. Besides, we generalized the notion of the ${ℛ}(p,q)$-elliptic Hermitian matrix model with an arbitrary conformal dimension $\mathrm{\Delta }$. Finally, we deduce relevant particular cases generated by quantum algebras known in the literature.

In this paper, the relation between the modified Lorenz boosts, proposed in the doubly relativity theories and a linear combination of Conformal Group generators in R^1,d-1 is investigated. The introduction of a new generator is proposed in order to deform the Conformal Group to achieve the connection conjectured. The new generator is obtained through a formal dimensional reduction from a free massless particle living in a R^2,d space. Due to this treatment it is possible to say that even DSR theories modify light-cone structure in R^1,d-1, it could remains, in some cases, untouched in R^2,d.

In this paper, we have studied the area and mass spectrum of a Lifshitz black hole in 2+1 dimensions. This black hole is obtained for conformal gravity in 2+1 dimensions and is asymptotic to z = 0 Lifshitz spacetime. Quasinormal modes (QNM) frequencies of the conformally coupled scalar field perturbations are employed for the purpose of analyzing the area spectrum of the black hole. We have used two methods: modified Hod's conjecture and Kunsttater's method. In both methods, the area and the mass spectrum is shown to be equally spaced. We compared our results with the area spectrum of the BTZ black hole and the z = 3 black hole and made suggestions to extend this work in the future.

The model of a point particle in the background of external symmetric tensor fields is analyzed from the higher spin theory perspective. It is proposed that the gauge transformations of the infinite collection of symmetric tensor fields may be read off from the covariance properties of the point particle action w.r.t. general canonical transformations. The gauge group turns out to be a semidirect product of all phase space canonical transformations to an Abelian ideal of "hyperWeyl" transformations and includes U(1) and general coordinate symmetries as a subgroup. A general configuration of external fields includes rank-0,1,2 symmetric tensors, so the whole system may be truncated to ordinary particle in Einstein–Maxwell backgrounds by switching off the higher-rank symmetric tensors. When otherwise all the higher rank tensors are switched on, the full gauge group provides a huge gauge symmetry acting on the whole infinite collection of symmetric tensors. We analyze this gauge symmetry and show that the symmetric tensors which couple to the point particle should not be interpreted as Fronsdal gauge fields, but rather as gauge fields of some conformal higher spin theories. It is shown that the Fronsdal fields system possesses twice as many symmetric tensor fields as is contained in the general background of the point particle. Besides, the particle action in general backgrounds is shown to reproduce De Wit–Freedman point particle–symmetric tensors first order interaction suggested many years ago, and extends their result to all orders in interaction, while the generalized equivalence principle completes the first order covariance transformations found in their paper, in all orders.

We show that logarithmic conformal field theories may be derived using nilpotent scale transformation. Using such nilpotent weights we derive properties of LCFT's, such as two and three point correlation functions solely from symmetry arguments. Singular vectors and the Kac determinant may also be obtained using these nilpotent variables, hence the structure of the four point functions can also be derived. This leads to non homogeneous hypergeometric functions. Also we consider LCFT's near a boundary. Constructing "superfields" using a nilpotent variable, we show that the superfield of conformal weight zero, composed of the identity and the pseudo identity is related to a superfield of conformal dimension two, which comprises of energy momentum tensor and its logarithmic partner. This device also allows us to derive the operator product expansion for logarithmic operators. Finally we discuss the AdS/LCFT correspondence and derive some correlation functions and a BRST symmetry.

The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit calculations are given for those contributions to the conformal anomaly which emerge as a result of free scalar propagation as well as from scalar self-interactions up to second order in the scalar self-coupling. The renormalization-group behavior of the theory is, subsequently, exploited in order to advance the evaluation of the conformal anomaly to third order in the scalar self-coupling. As a direct consequence the effective action is evaluated to the same order. In effect, complete contributions to the theory's conformal anomaly and effective action are evaluated up to fourth-loop order.

We discuss tachyon-free examples of (Type IIB on) noncompact nonsupersymmetric orbifolds. Tachyons are projected out by discrete torsion between orbifold twists, while supersymmetry is broken by a Scherk–Schwarz phase (+1/-1 when acting on space–time bosons/fermions) accompanying some even order twists. The absence of tachyons is encouraging for constructing nonsupersymmetric D3-brane gauge theories with stable infrared fixed points. The D3-brane gauge theories in our orbifold backgrounds have chiral supersymmetric spectra, but nonsupersymmetric interactions.

In this brief talk, I will try to focus on the things that happened at the conference that seemed very important, but that I didn’t understand.

The microelectromechanical system (MEMS) quasi-end-fire array antenna based on a liquid crystal polymer (LCP) substrate is designed and fabricated in this paper. The maximum radiation direction of the antenna tends to the cone axis forming an angle less than 90${}^{\circ }$, which satisfies the proximity detection system applied at the forward target detection. Furthermore, the proposed antenna is fed at the ended side in order to save internal space. Moreover, the proposed antenna takes small covering area of the proximity detection system. The proposed antenna is fabricated by using the flexible MEMS process, and the measurement results agree well with the simulation results. This is the first time that a conical conformal array antenna is fabricated by the flexible MEMS process to realize the quasi-end-fire radiation. A pair of conformal MEMS array antennas resonates at 14.2 GHz with its mainlobes tending to the cone axis forming a 30${}^{\circ }$ angle and a 31${}^{\circ }$ angle separately, and the gains achieved are 1.82 dB in two directions, respectively. The proposed antenna meets the performance requirements for the proximity detection system which has vast application prospects.

This paper deals with the design, simulation, and practical modeling of metamaterial-based multiband conformal bandpass filter (BPF) for various wireless communication applications with improved quality factors. The novel metamaterial in the form of a split ring resonator is loaded on the ground plane face of the proposed BPF. The overall dimension of the designed BPF is only $28\times 28{\mathrm{\text{mm}}}^2$. The proposed BPF is tuned initially for quality factor enhancement based on the thickness of the substrate, physical parameters of the f transmission line, ground plane, externally loaded elements, and the gap in the metamaterial loading. The suggested filter operates at triple band covering the frequency bands from 1.4 to 2.2, 3.6 to 3.9, and 4.8 to 5.9GHz, which are suitable for sub-6GHz 5G and other wireless applications. The insertion loss is observed as 1dB, which is suitable for the proposed BPF. The conformal behavior of the filter is judged through bending deformation analysis at various bending positions like (15${}^{\circ }$, 30${}^{\circ }$, 45${}^{\circ }$, 60${}^{\circ }$, and 90${}^{\circ }$). The proposed BPF retains triple pass band characteristics at various bending deformations, which makes it suitable to be used in curved structures or flexible circuitry. The theory of equivalent circuits and quality factor $(Q)$ of the designed BPF is discussed in this paper. The results are analyzed experimentally through ANRITSU-MS2037C combinational analyzer. The proposed BPF is suitable for sub-6 GHz 5G, WLAN, and Wi-Max applications.

We study knots in 𝕊³ obtained by the intersection of a minimal surface in ℝ⁴ with a small 3-sphere centered at a branch point. We construct new examples of minimal knots. In particular we show the existence of non-fibered minimal knots. We show that simple minimal knots are either reversible or fully amphicheiral; this yields an obstruction for a given knot to be a simple minimal knot. Properties and invariants of these knots such as the algebraic crossing number of a braid representative and the Alexander polynomial are studied.

The interaction of dark energy and dark matter has been studied widely using various formalisms in an effort to understand the physics of such gravitational interactions. Such studies are motivated by the idea that they might hold the key to resolving some of the outstanding problems in cosmology. We will consider the relativistic convective variational formalism in our study of dark matter (hereafter DM)-dark energy (hereafter DE) interaction. In particular, we go beyond the gravitational interaction and consider the potential entrainment phenomena involving the two dark-sector constituents. Ours is a formalism paper and focuses on the theoretical considerations that inform the modeling of such interactions.

Carlotto, Chodosh and Rubinstein studied the rate of convergence of the Yamabe flow on a closed (compact without boundary) manifold $M$:

Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no measurable size changes, while a postulate for probabilistic evolution leads to physical dilatations manifested as measurable phase changes. Our results lead to the Feynman path integral formulation, from which follows the Schrödinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures — the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.

Conformal, concircular, quasi-conformal and conharmonic curvature tensors play an important role in Riemannian geometry. In this paper, we study on normal complex contact metric manifolds under flatness conditions of these tensors.

The complete structure of the Casimir ${{𝒲}{𝒜}}_N$ algebras is shown to exist in such a way that the Casimir ${{𝒲}{𝒜}}_N$ algebra is a kind of truncated type of ${{𝒲}}_{\infty }$ algebra both in the primary and in the quadratic basis, first using the associativity conditions in the basis of primary fields and second using the Miura basis coming from the free field realization as a different basis. We can conclude that the Casimir ${{𝒲}{𝒜}}_N$ algebra is a kind of truncated type of ${{𝒲}}_{\infty }$ algebra, so it is clear from any construction of ${{𝒲}}_{\infty }$ algebra that by putting infinite number of fields $W_s$ with $s>N$ to zero, we arrive at the Casimir ${{𝒲}{𝒜}}_N$ algebra. We concentrated in this work only for the particular case of ${{𝒲}{𝒜}}_5$ algebra since this example gives us explicitly a method on how to deal with the general case $N$.

With the extended navigation data, we consider the generalized Zermelo navigation on Riemannian manifolds, admitting a space-dependent ship’s speed in the presence of perturbation determined by a weak velocity vector field, with application of Finsler metric of Randers type. The approach is shown via indicatrix and inner product. We also compare our findings in the context of conformality for the cases of weak and critical winds. The study is illustrated with the example in dimension 2.

The Barbero-Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose physical significance is as-of-yet unknown. It is an inherent characteristic of the quantum theory since it appears in the spectra of geometric operators. The parameter’s appearance in the area and volume spectra imply that it plays a role in determining the fundamental length scale of space. This appearance as a rescaling of lengths motivates a possible conformal interpretation. Presented here is an analysis of the conformal scaling of the triad formalism and the revelation that the Barbero-Immirzi parameter precisely corresponds to the conformal scale factor. Furthermore, at the kinematical level the conformal scale factor materializes as a scalar field coupled to gravity. The development of this conformal scalar field to the quantum sector of the theory is also sketched.

In this brief talk, I will try to focus on the things that happened at the conference that seemed very important, but that I didn’t understand.