On stringy thresholds in SYM/AdS thermodynamics

We consider aspects of the role of stringy scales and Hagedorn temperatures in the correspondence between various field theories and AdS-type spaces, The boundary theory is set on a toroidal world-volume to enable small scale s to appear in the supergravity backgrounds also for low field-theory tempe ratures. We find that thermodynamical considerations tend to favour backgro und manifolds with no string-size characteristic scales. The gravitational dynamics censors the reliable exposure of Hagedorn physics on the supergrav ity side, and the system does not allow the study of the Hagedorn scale by low-temperature field theories, These results are obtained following some h euristic assumptions on the character of stringy modifications to the gravi tational backgrounds. A rich phenomenology appears on the supergravity side , with different string backgrounds dominating in different regions, which should have field-theoretic consequences. Six-dimensional world-volumes tur n out to be borderline cases from several points of view. For lower-dimensi onal world-volumes, a fully holographic behaviour is exhibited to order 1/N -2, and open strings in their presence are found to have a thermodynamic Ha gedorn behaviour similar to that of closed strings in flat space. (C) 1999 Published by Elsevier Science B.V.