We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satis...

3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean transformation groups. This paper introduces a novel method to classify surfaces by conformal transformation groups. Conformal equivalent clas...

If the conformal holonomy group Hol(T) of a simply connected space with conformal structure of signature (2p−1, 2q−1) is reduced to U(p, q) then the conformal holonomy is already contained in the special unitary group SU(p, q). We present two different proofs of this statement, one using conformal tractor calculus and an alternative proof using Sparling’s characterisation of Fefferman metrics.

In this paper we introduce and explore conformal parabolic iterated function systems. We deene and study topological pressure, Perron-Frobenius type operators, semi-conformal and conformal measures and the Hausdorr dimension of the limit set. With every parabolic system we associate an innnite hyperbolic conformal iterated function system and we employ it to study geometric and dynamical featur...

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to describe in further detail the holonomy of the adapted Weyl connection on conformal products. 2000 Mathematics...

Using conformal coordinates associated with projective conformal relativity we obtain a conformal Klein-Gordon partial differential equation. As a particular case we present and discuss a conformal ‘radial’ d’Alembert-like equation. As a by-product we show that this ‘radial’ equation can be identified with a one-dimensional Schrödinger-like equation in which the potential is exactly the second ...

To leading order in CX~ ( Q2), conformal symmetry specifies the eigensolutions of the evolution equation for meson distribution amplitudes, the wavefunctions which control large-momentum-transfer exclusive mesonic processes in &CD. We find that at next to leading order, the eigensolutions in various field theories depend on the regularization scheme, even for zero p-function. This is contrary t...

The conformal loop ensembles CLEκ, defined for 8/3 ≤ κ ≤ 8, are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compu...

We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an ‘existence proof’ that this is indeed possible we show how to derive N = 4 super Yang Mills theory with any compact gauge group G from non-conformal gauged N = 4 supergravity as a special flat space limit. We stress the role that the anticipa...

The scalar-tensor theory is plagued by nagging questions if different conformal frames, in particular the Jordan and Einstein conformal frames, are equivalent to each other. As a closely related question, there are opposing views on which of the two conformal frames is physically acceptable. Reinforcing our previous claims, we offer replies based on a cosmological model of the scalar-tensor the...