We prove that k-trace operators of SO(6)R irreps with Young tableau partitions {r1, r2, r3}, constructed out of k chiral primaries in the twenty dimensional SO(6)R irrep, lead to quasi primary fields with protected conformal dimensions under certain conditions. If r1, r2, r3 are all even, r1 + r2 + r3 = 2k and the field is a spacetime scalar, then the conformal dimension 2k is unrenormalized. I...

I review recent work on the holographic relation between higher-spin theories in Anti-de Sitter spaces and conformal field theories. I present the main results of studies concerning the higher-spin holographic dual of the three-dimensional O(N) vector model. I discuss the special role played by certain double-trace deformations in Conformal Field Theories that have higher-spin holographic duals...

A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be achieved in a space of Lagrangians differing only by a field dependent conformal factor. In particular the Noether currents and the quantum constraints can be d...

A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as B-metric manifold), which obtained by a contact conformal transformation of the Reeb vector field, its dual 1-form, B-metric, and associated B-metric. case in potential torse-forming field constant length vertical distribution determined studied. In this way, manifolds from one main classes studied ar...

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

We study the effect of a nontrivial conformal vector field on geometry compact Riemannian spaces. find two new characterizations m-dimensional sphere Sm(c) constant curvature c. The first characterization uses well known de-Rham Laplace operator, while second solution famous Fischer–Marsden differential equation.

The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy momentum tensor. Ward identities resulting from conformal invariance are discussed. Explicit expressions for two and three point functions, which are essenti...

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R × R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over V L ⊗ V R , where V L and V R are two vertex operat...