On QCD String Theory and AdS Dynamics

The AdS/CFT correspondence of elementary string theory has been recently suggested as a ``microscopic'' approach to QCD string theory in various dimensions. We use the microscopic theory to show that the ultraviolet regime on the string world-sheet is mapped to the ultraviolet effects in QCD. In the case of QCD_2, a world-sheet path integral representation of QCD strings is known, in terms of a topological rigid string theory whose world-sheet supersymmetry is reminiscent of Parisi-Sourlas supersymmetry. We conjecture that the supersymmetric rigid string theory is dual to the elementary Type IIB string theory in the singular AdS background that corresponds to the large-N limit of QCD_2. We also generalize the rigid string with world-sheet Parisi-Sourlas supersymmetry to dimensions greater than two, and argue that the theory is asymptotically free, a non-zero string tension is generated dynamically through dimensional transmutation, and the theory is topological only asymptotically in the ultraviolet.