U-Duality and Symplectic Formulation of Dilaton-Axion Gravity

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We study a bosonic four--dimensional effective action corresponding to the heterotic string compactified on a 6--torus (dilaton--axion gravity with one vector field) on a curved space--time manifold possessing a time--like Killing vector field. Previously an existence of the SO(2,3) Sp(4, R) global symmetry (U--duality) as well as the symmetric space property of the corresponding σ--model have been established following Neugebauer and Kramer approach. Here we present an explicit form of the Sp(4, R) generators in terms of coset variables and construct a representation of the coset in terms of the physical target space coordinates. Complex symmetric 2× 2 matrix Z (``matrix dilaton --axion'') is introduced for which U--duality takes the matrix valued SL(2, R) form. In terms of this matrix the theory is further presented as a Kähler σ--model. This leads to a more concise 2× 2 formulation which opens new ways to construct exact classical solutions. New solution (corresponding to constant Im Z) is obtained which describes the system of point massless magnetic monopoles endowed with axion charges equal to minus monopole charges. In such a system mutual magnetic repulsion is exactly balanced by axion attraction so that the resulting space time is locally flat but possesses multiple Taub--NUT singularities.