UNIFIED EINSTEIN-VIRASORO MASTER EQUATION IN THE GENERAL NONLINEAR SIGMA-MODEL

The Virasoro master equation (VME) describes the general affine-Viraso ro construction T = L(ab)J(a)J(b) + iD(a) partial derivative J(a) in t he operator algebra of the WZW model, where L(ab) is the inverse inert ia tensor and D-a is the improvement vector. In this paper, we general ize this construction to find the general (one-loop) Virasoro construc tion in the operator algebra construction to find the general (one-loo p) Virasoro construction in the operator algebra of the general nonlin ear sigma model. The result is a unified Einstein-Virasoro master equa tion which couples the space-time spin-1 field L(ab) to the background fields of the sigma model. For a particular solution L(G)(ab), the un ified system reduces to the canonical stress tensors and conventional Einstein equations of the sigma model, and the system reduces to the g eneral affine-Virasoro construction and the VME when the sigma model i s taken to be the WZW action. More generally, the unified system descr ibes a space of conformal field theories which is presumably much larg er than the sum of the general affine-Virasoro construction and the si gma model with its canonical stress tensors. We also discuss a number of algebraic and geometrical properties of the system, including its r elation to an unsolved problem in the theory of G-structures on manifo lds with torsion.