The Effect of Conformal Symmetry on Charged Wormholes

This paper discusses the effect that conformal symmetry can have on a charged wormhole. The analysis yields a physical interpretation of the conformal factor in terms of the electric charge. The rate of change of the conformal factor determines much of the outcome, which ranges from having no solution to wormholes having either one or two throats.

Twofold hidden conformal symmetry of Kerr-Bolt black holes

Previously we have shown that a four-dimensional Kerr-Bolt black hole in non-extremal and also in extremal cases could be described by a holographic two-dimensional （2D） conformal field theory （CFT） [Ghezelbash A M, Kamali V and Setare M R 2010 Phys. Rev. D 82 124051; Setare M R and Kamali V 2010 JHEP 10 074]. Motivated by recent work [Chen C M, Huang Y M, Sun J R, Wu M F and Zou S J 2010 Phys. Rev. D 82 066004], we show that there is another holographic description for these black holes. The first description is called the J-picture, whose construction is based on the black hole angular momentum. The new description is called the Q-picture, whose constructions originate from the nut charge of the black hole. Similar to the previous cases [Ghezelbash A M, Kamali V and Setare M R 2010 Phys. Rev. D 82 124051; Setare M R and Kamali V 2010 JHEP 10 0741, we show that this new picture for a low frequency limit of the wave equation of a massless charged scalar field in the background of a Kerr-Bolt black hole can be written as the Casimir of SL（2, R） symmetry. Our result shows that the entropy of the black hole is reproduced by the Cardy formula. In addition, the absorption cross section is consistent with the finite temperature absorption cross section for a two-dimensional CFT.

Hidden conformal symmetry and pair production near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter spacetime

We show that the study of the hidden conformal symmetry that is associated with the Kerr/CFT correspondence can also apply to the cosmological horizon in the Kerr-Newman-Taub-NUT-de Sitter spacetime.This symmetry allows employing some two dimensional conformal field theory methods to understand the properties of the cosmological horizon.The entropy can be understood by using the Cardy formula,and the equation for the scattering process in the near region is in agreement with that obtained from a two point function in the two-dimensional conformal field theory.We also show that pair production can occur near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter for near extremal conditions.

Momentum as Translations at Conformal Infinity

Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.

Cosmic inflation from broken conformal symmetry

A period of rapidly accelerating expansion is expected in the early Universe implemented by a scalar field slowly rolling down along an asymptotically flat potential preferred by the current data.In this paper,we point out that this picture of the cosmic inflation with an asymptotically flat potential could emerge from the Palatini quadratic gravity by adding the matter field in such a way to break the local gauged conformal symmetry in both kinetic and potential terms.

Conformable fractional heat equation with fractional translation symmetry in both time and space

We investigate the fractional heat equation with fractional translation in both time and position with different fractional orders.As examples,we consider a rod and anα-disk with an initial constant temperature and discuss their cooling processes in the examined formalism.

New wormhole model with quasi-periodic oscillations exhibiting conformal motion in f(T,T)gravity

This analysis explores the new wormhole(WH)solution in the background of teleparallel gravity with minimal matter coupling.To complete this study,we consider the conformal symmetry with non-zero Killing vectors.The exact shape function is computed by considering the linear equation of state with the phantom regime.The energy conditions are investigated for the calculated shape function with the equation of state parameter.The presence of exotic matter is confirmed due to the violation of the null energy condition.The current study also explores the physical properties of the epicyclic frequencies with quasi-periodic oscillations.In the astrophysical,epicyclic frequencies are extensively employed to explore the self-gravitating system.It is concluded that a stable WH solution is acceptable for WH geometry.

Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation

Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method（GCTM）. The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor（DSCF） becomes singular when the inhomogeneity parameter of medium is close to zero.

Lie Symmetries of Klein-Gordon and Schrodinger Equations

In this paper, we investigate the Lie point symmetries of Klein-Gordon equation and Schr?dinger equation by applying the geometric concept of Noether point symmetries for the below defined Lagrangian. Moreover, we organize a strong relationship among the Lie symmetries related to Klein-Gordon as well as Schr?dinger equations. Finally, we utilize the consequences of Lie point symmetries of Poisson and heat equations within Riemannian space to conclude the Lie point symmetries of Klein-Gordon equation and Schr?dinger equation within universal Riemannian space.

Unified interpretation of scalegenesis in conformally extended standard models:a dynamical origin of Higgs portal

We present a universal interpretation of a class of conformal extended standard models that include Higgs portal interactions as realized in low-energy effective theories.The scale generation mechanism in this class(scalegenesis)arises along the(nearly)conformal/flat direction for breaking scale symmetry,where the electroweak symmetry-breaking structure arises similarly as in the standard model.A dynamical origin for the Higgs portal coupling can provide the discriminator for the low-energy“universality class,”to be probed in forthcoming collider experiments.

New Algebraic Structures from Hermitian One-Matrix Model

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory （CFT） method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.

Super W_(1+∞) n-Algebra in the Supersymmetric Landau Problem

We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generalized super Bremner identity.For the infinite conserved operators in the supersymmetric Landau problem,we derive the super W_(1+∞) n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases,respectively.Moreover the super W_(1+∞) sub-2n-algebra is also given.