Recent progress in the theory of noncritical strings

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We compare the results of analytical and numerical studies of lattice 2D quantum gravity, where the internal quantum metric is described by random (dynamical) triangulation, with the recent results of conformal approach developed by Knizhnik, Polyakov and Zamolodchikov. The remarkable agreement is underlined for the interactions of gravity with matter fields: Potts spins, D-dimensional Gaussian fields (bosonic string). Some new results are presented for D = 1 discretized bosonic strings satisfying the predictions of conformal theory for the critical exponents: γ str = 0, ν str = 0, but with unusual logarithmic corrections.