Let V L and V R be simple vertex operator algebras satisfying certain natural uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let F be a conformal full field algebra over V L ⊗ V . We prove that the qτ -qτ -traces (natural traces involving qτ = e2πiτ and qτ = e2πiτ ) of geometrically modified genus-zero correlation functions for F are convergent in suitable regions a...

Inflationary scenario based on a renormalizable model of conformal gravity is proposed and primordial spectrum is derived. The sharp fall off of the angular power spectra at low multipoles in the COBE and WMAP observations are explained by a dynamical scale of quantum gravity. At this scale, the universe would make a sharp transition from the quantum spacetime with conformal invariance to the c...

Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while the latter quantifies their tendency to form logarithmic spirals. We show how these characteristics are related to local operators of conformal field theory a...

We consider the non-interacting massive Wess-Zumino model in four-dimensional anti-de Sitter space and show that the conformal dimensions of the corresponding boundary fields do not always satisfy the relation expected from superconformal invariance.

Invariance under finite conformal transformations in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of vertex algebra to higher dimensions. Gibbs (finite temperature) expectation values appear as elliptic functions in the conformal time. We survey and further pursue our progra...

The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the solution of the BFKL equations both in the transverse coordinate and momentum spaces. This result is obtained from the solution of the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being the product of an holo...

Using the dipole framework for QCD at small xBj in the 1/Nc limit, we derive the expression of the 1→p dipole multiplicity density in momentum space. This gives an analytical expression for the 1→p QCD Pomeron amplitudes in terms of one-loop integration of effective vertices in transverse momentum. Conformal invariance and a Hilbert space construction for dipole correlation functions are the ma...

The odderon equation is studied in terms of the variable suggested by the modular invariance of the 3 Reggeon system. Odderon charge is identified with the cross-product of three conformal spins. A complete set of commuting operators: ĥ2 and q̂ is diagonalized and quantization conditions for eigenvalues of the odderon charge q̂ are solved for arbitrary conformal weigth h. PACS: 12.38.Cy; 11.55.Jy.

Using the dipole picture describing the 1/NC limit of QCD at small x and the conformal invariance properties of the BFKL kernel in transverse coordinate space, we show that the 1→p dipole densities can be expressed in terms of dual ShapiroVirasoro amplitudes B2p+2 and their generalization including non-zero conformal spins. We discuss the possibility of an effective closed string theory of inte...

We study the su(2) conformal field theory in its spinon description, adapted to the Yangian invariance. By evaluating the action of the Yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with su(2) spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible Yangian...