LARGE CONFORMAL-INVARIANCE AND DUALITY IN SELF-DUAL GRAVITY AND (2,1)HETEROTIC STRING THEORY

A system of gravity coupled to a 2-form gauge field, a dilaton and Yan g-Mills fields in 2n dimensions arises from the (2,1) sigma model or s tring. The field equations imply that the curvature with torsion and Y ang-Mills field strength are self-dual in four dimensions, or satisfy generalised self-duality equations in 2n dimensions. The Bom-Infeld-ty pe action describing this system is simplified using an auxiliary metr ic and shown to be classically Weyl invariant only in four dimensions. A dual form of the action is found (no isometries are required). In f our dimensions, the dual geometry is self-dual gravity without torsion coupled to a scalar field. In D>4 dimensions, the dual geometry is he rmitian and determined by a D-4 form potential K, generalising the Kah ler potential of the four dimensional case, with the fundamental 2-for m given by (J) over tilde = i <partial derivative(partial derivative) over bar K>. The coupling to Yang-Mills is through a term K boolean AN D tr(F boolean AND F) and leads to a Uhlenbeck-Yau field equation (J) over tilde(ij)F(ij) = 0. (C) 1998 Elsevier Science B.V.