In 1981 Polyakov [1,2] showed that the integration measure over surfaces embedded into flat space-times of dimension D not equal to 26 ( or 10), involves an additional scalar field with an exponential potential. With this motivation I, together with A. Neveu [3–8] and A. Bilal [9–12], extensively studied this so-called Liouville dynamics and developed the associated string theories, which are of a novel type. As we shall see, two new critical values of the space-time dimension D appea, r both for the purely bosonic and for the Neveu-Schwarz-Ramond (NSR) case. They are equal to 7 and 13, and to 3 and 5 respectively. Our results possess an interesting structure which I intend to summarize, as much as posssible, in the present lecture notes.
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