Abstract
The non-linear sigma model of the dimensionally reduced Einstein (-Maxwell) theory is diagonally embedded into that of the two-dimensional heterotic string theory. Consequently, the embedded string backgrounds satisfy the (electromagnetic) Ernst equation. In the pure Einstein theory, the Matzner-Misner SL(2, R ) transformation can be viewed as a change of the conformal structure of the compactified flat two-torus, and in particular its integral subgroup SL(2, Z ) acts as the modular transformation. The Ehlers SL(2, R ) and SL(2, Z ) similarly act on another torus whose conformal structure is induced through the Kramer-Neugebauer involution. Either of the Matzner-Misner and the Ehlers SL(2, Z ) can be embedded to a special T-duality, and if the former is chosen, then the Ehlers SL(2, Z ) is shown to act as the S-duality on the four-dimensional sector. As an application we obtain some new colliding string wave solutions by using this embedding as well as the inverse scattering method.
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