Abstract The conformal bridge transformation (CBT) is reviewed in the light of PT symmetry. Originally, CBT was presented as a non-unitary (a complex canonical classical case) that relates two different forms dynamics sense Dirac. Namely, it maps a...

A conformal transformation is a diffeomorphism which preserves angles; the differential at each point is the composition of a rotation and a dilation. In its original sense, conformal geometry is the study of those geometric properties preserved under transformations of this type. This subject is deeply intertwined with complex analysis for the simple reason that any holomorphic function f(z) o...

The solutions of two-dimensional gravity following from a non– linear Lagrangian L = f(R)√g are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of twodimensional Einstein-dilaton gravity and vice versa. KEY : Dilaton gravity in 1+1 dimensions, exact solutions, Birkhoff theorem, ...

The anomalous conformal transformation law of the generalized entropy is found for dilaton gravity coupled to a 1+1 conformal matter sector with central charges c = c̃. (When c 6= c̃ the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, S′′ gen + (6/c)(S ′ out) , is primary, and therefore retains its sign under a ge...

Deformations of surfaces with the same intrinsic shape can often be described accurately by a conformal model. A major focus of computational conformal geometry is the estimation of the conformal mapping that aligns a given pair of object surfaces. The uniformization theorem enables this task to be acccomplished in a canonical 2D domain, wherein the surfaces can be aligned using a Möbius transf...

A novel robust adaptive beamforming method for conformal array is proposed. By using interpolation technique, the cylindrical conformal array with directional antenna elements is transformed to a virtual uniform linear array with omni-directional elements. This method can compensate the amplitude and mutual coupling errors as well as desired signal point errors of the conformal array efficientl...

In this article we will invetsigate the origin of central charges in the Poisson algebra of charges, which arise in dimensionally reduced theories describing black holes. In order to do this we will analyze the equations of motion arising from the dimensionally reduced EinsteinHilbert action with the ansatz of spherical symmetry. We will show that the equations of motion and the constraints, wh...

We show that any conformal field theory in d-dimensional Minkowski space, in a phase with spontaneously broken conformal symmetry and with the dilaton among its fields, can be rewritten in terms of the static gauge (d − 1)-brane on AdS(d+1) by means of an invertible change of variables. This nonlinear holographic transformation maps the Minkowski space coordinates onto the brane worldvolume one...