The Virasoro master equation describes a large set of conformal field
theories known as the affine-Virasoro constructions, in the operator algebra
(affine Lie algebra) of the WZW model, while the Einstein equations of the
general non-linear sigma model describe another large set of conformal field
theories. This talk summarizes recent work which unifies these two sets of
conformal field theories, together with a presumable large class of new
conformal field theories. The basic idea is to consider spin-two operators of
the form Lijββxiβxj in the background of a general
sigma model. The requirement that these operators satisfy the Virasoro algebra
leads to a set of equations called the unified Einstein-Virasoro master
equation, in which the spin-two spacetime field Lijβ couples to the usual
spacetime fields of the sigma model. The one-loop form of this unified system
is presented, and some of its algebraic and geometric properties are discussed.Comment: 18 pages, Latex. Talk presented by MBH at the NATO Workshop `New
Developments in Quantum Field Theory', June 14-20, 1997, Zakopane, Polan