THE ALGEBRA OF THE ENERGY-MOMENTUM TENSOR AND THE NOETHER CURRENTS INCLASSICAL NONLINEAR SIGMA-MODELS

The recently derived current algebra of classical non-linear sigma mod els on arbitrary Riemannian manifolds is extended to include the energ y-momentum tensor. It is found that in two dimensions the energy-momen tum tensor theta(munu), the Noether current j(mu) associated with the global symmetry of the theory and the composite field 3 appearing as t he coefficient of the Schwinger term in the current algebra, together with the derivatives of j(mu) and j, generate a closed algebra. The su balgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge c = 0, reflecting the classical conformal invariance o f the theory, but the current algebra part and the semidirect product structure are quite different from the usual KacMoody/Sugawara type co nstruction.