We will describe the appearance of specific algebraic KdV potentials as a consequence of a requirement on a integro-differential expression. This expression belongs to a class generated by means of Virasoro vector fields acting on the KdV field. The “almost” rational KdV fields are described in terms of a geometrical locus of complex points. A class of solutions of this locus has recently appea...

A ‘canonical mapping’ is established between the c = −1 system of bosonic ghosts and the c = 2 complex scalar theory and, a similar mapping between the c = −2 system of fermionic ghosts and the c = 1 Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective c < 0 and c > 0 theories share the same space of states, wherea...

Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial...

In the context of two-dimensional quantum cosmology, we consider the pathintegral of a string on annulus which contains the Liouville field and conformal matter fields. We show that, in the transition amplitude of the string universe, the non-zero modes of the fields are all cancelled out only when we take the c = 1 conformal matter field and impose the Neumann boundary condition on the system....

A generalization of the limiting procedure of Penrose, which allows non-zero cosmological constants and takes into account metrics that contain homogeneous functions of degree zero, is presented. It is shown that any spacetime which admits a spacelike conformal Killing vector has a limit which is conformal to plane waves. If the spacetime is an Einstein space, its limit exists only if the cosmo...

We consider Einstein Gravity coupled to matter consisting of a gauge field with any compact gauge group and coupled scalar fields. We investigate under what conditions a free specification of a spatial field configuration and its time derivative determines a solution to the field equations (thin-sandwich problem). We establish sufficient conditions under which the thin-sandwich problem can be s...

Consequences of the existence of conformal vector fields in (locally) symmetric and conformal symmetric spaces, have been obtained. An attempt has been made for a physical interpretation of the consequences in the framework of general relativity.

We give necessary and suucient conditions for a conformal foliation locally generated by conformal vector elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Also we obtain reducibility results for harmonic morphisms induced by (innnitesimal) conformal actions on Einstein manifolds.