Some years ago, Polyakov [1] proposed constructing all conformally invariant quan tum field theories by using the constraint of conformal invariance to make concrete the fundamental principles of quantum field theory. This is the conformal boots t rap program. Conformal field theories describe the universality classes of critical phenomena, or equivalently the short distance limits of quantum f...

This is a survey about conformal mappings between pseudo-Riemannian manifolds and, in particular, conformal vector fields defined on such. Mathematics Subject Classification (2000). Primary 53C50; Secondary 53A30; 83C20.

The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT’s) and vertex operator algebras (VOA’s). This cohomology theory produces a number of invariants of CFT’s and VOA’s, one of which is the space of their infinitesimal deformations. The paper is inspired by the ideas of Drinfeld [5],...

In the last decade, contact, almost contact, paracontact cosymplectic, and conformal cosymplectic manifolds carrying κ > 1 structure vector fields ξ have been studied by many authors, e.g. [2], [7], [11], [15]. In the present paper we consider a (2m + 2)-dimensional Riemannian manifold carrying two structure vector fields ξ (r ∈ {2m+1, 2m+2}), a (1, 1)-tensor field Φ, and a structure 2 form Ω o...

We consider the massless minimally coupled scalar field in de Sitter ambient space formalism as a gauge potential or connection field. construct theory by helping an arbitrary constant five-vector $B^\alpha$ analogous to standard theory. The Lagrangian density of interaction between and spinor fields is presented this framework. Yukawa can be extracted from at null curvature limit appropriate c...

We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector of two-dimensional quantum gravity coupled to an ordinary conformal field theory in the conformal gauge. We also examine, in the (p, q) minimal conformal fie...