Narrow Results

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.

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.

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.

We present a minimal candidate model for the composite Higgs mechanism with fermion doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group.³ The model is known to be close to the conformal window with a small β-function.⁴ Chiral symmetry breaking with vacuum condensate becomes the origin of electroweak symmetry breaking from compositeness. Close to the conformal window, a light scalar state with Higgs quantum numbers is emerging. Associations with the recently observed 126 GeV Higgs boson, or with a dilaton state from broken scale invariance, are subjects of ongoing investigations.

To integrate conformal antenna system on surface vessel, we must deal with some key problem, first is the solution, second the development platform, and third the approaches based on the solution and platform, for the design of antenna, and solve issues of details, such as reduce the kind and number of antenna, furthermore, the bulk of the antenna on a ship, to realize the electromagnetic stealth meeting the requirements of warship. Methods: the development framework had been built, including model of antenna, software radio and cognitive radio framework, as well as development platform which is an adaptive simulating and design platform based on distribution and parallel system, to realize the phased array, optimize the placement of array elements and whole structure of the planar, calculate the feature of material in needs which call different EM software in the proper time automatically. Furthermore, the series methods to solve the key technology such as signal processing algorithm and spectrum management had been proposed, including thinking of the top-level design, and modularity of approaches, as well as the technique of semi-physical simulation. Results: The framework and methods meet the requirement for seamless RF integration of the conformal antenna system, in which all the output are met the demand of design. For example, in 3.8-4.0GHz frequency band, the antenna parameters is as follows: horizontal omnidirectional gain 6dBi, directional beam gain 22dBi, VSWR 2, sidelobe level of horizontal plane −22dB, impeadance=50, number of planar=6, elements in each planar=128. Conclusion: The framework and methods brings many innovations, including not only design concept and design methods, but also design platform and design results which have many advantages such as high reliability and intelligence, strong stability and extendibility, as well as self-adapting.