Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space–time dimensions implies the Huygens’ principle, and hence, rationality of correlation functions of observable fields [29]. The conformal Hamiltonian H has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space ...

the mathematical aspect of cartographic mapping is a process which establishes a unique connection between points of the earth’s sphere and their images on a plane. it was proven in differential geometry that an isometric mapping of a sphere onto a plane with all corresponding distances on both surfaces remaining identical can never be achieved since the two surfaces do not possess the same gau...

We study conformal theories of gravity, i.e. those whose action is invariant under the local transformation gμν → ω(x)gμν . As is well known, in order to obtain Einstein gravity in 4D it is necessary to introduce a scalar compensator with a VEV that spontaneously breaks the conformal invariance and generates the Planck mass. We show that the compactification of extra dimensions in a higher dime...

We define extended SL(2,R)/U(1) characters which include a sum over winding sectors. By embedding these characters into similarly extended characters of N = 2 algebras, we show that they have nice modular transformation properties. We calculate the modular matrices of this simple but non-trivial non-rational conformal field theory explicitly . As a result, we show that discrete SL(2,R) represen...