Singular Limits and String Solutions

It is shown that new leading (0) as well as all-order solutions of String theory can be obtained by taking appropriate singular limits of the known solutions. We give several leading order solutions for the bosonic as well as the heterotic string. We then present all-order forms of the previously known two dimensional cosmological solutions. An all-order form for the cosmological solution in three dimensions is also predicted. The physical implications of our results are discussed. Classical solutions of string theory and their physical implications have been explored extensively recently. The search for the solutions of string theory has been done mainly along two lines. First, several leading order (0) solutions have been obtained by solving the equations of motion of the string eeective action or the vanishing of the one-loop-function equations 1;2. However this has the drawback of ignoring important stringy eeects. The exact string solutions in the curved background, on the other hand, are derived from the Lagrangians of several exact conformal eld theories, such as WZW and coset conformal eld theories 3;4. In this work we show that appropriate singular limits of the above backgrounds, both exact as well as eeective (leading order solution), give rise to new consistent solutions of string theory. The backgrounds generated in this way are not equivalent to the original ones. For example, by writing the two dimensional black hole in an appropriate coordinate system, the two dimenional cosmological solution 5 and the Liouville theory can be obtained by taking two diierent limits. Inspired by this result, we take singular limits in various other physical circumstances and obtain new solutions. A set of three dimensional cosmological backgrounds are obtained in this way from the 3-D black string 6. Similarly, a new solution is derived from the two dimensional charged black hole of the heterotic string theory 7. These solutions are characterized by the vanishing of the corresponding cosmological constant. One can also extract all-order solutions of string theory in this manner. In this paper we have given the all-order extension of the 2-D cosmological solution 5. The singular limit of the exact three dimensional black string 8 also generates cosmological backgrounds which we conjecture to be exact to all orders. We believe that our results can also be used in further classiication of the solutions of string theory. Earlier, it has been shown that a number of such solutions can be classiied …