String theory and classical integrable systems

Details String theory and classical integrable systems String theory and classical integrable systems

1994-04-20

arxiv.org/abs/hep-th/9404126v1

Physics

High Energy Physics

High Energy Physics - Theory

lecture given at III Baltic Rim student seminar, Helsinki, September 1993} 33pp, latex

Scientific paper

10.1007/3-540-58453-6_11

We discuss different formulations and approaches to string theory and $ 2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $ 2d$ conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of possible generalizations to ``higher-dimensional" models are made. We also speculate on the possible appearence of quantum integrable structures in string theory.

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