On Stringy Thresholds in SYM/AdS Thermodynamics

TL;DR

This paper explores how stringy scales and Hagedorn temperatures influence the thermodynamics of AdS spaces and their dual field theories, revealing limitations on observing Hagedorn physics and rich background phenomenology.

Contribution

It demonstrates that gravitational dynamics restrict the exposure of Hagedorn physics in supergravity backgrounds and identifies different dominant string backgrounds affecting field theory behavior.

Findings

Low-temperature field theories cannot reliably probe Hagedorn scales.

Different string backgrounds dominate in various regions, affecting dual field theories.

Open strings exhibit Hagedorn behavior similar to closed strings in flat space.

Abstract

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 scales to appear in the supergravity backgrounds also for low field-theory temperatures. We find that thermodynamical considerations tend to favour background manifolds with no string-size characteristic scales. The gravitational dynamics censors the reliable exposure of Hagedorn physics on the supergravity side, and the system does not allow the study of the Hagedorn scale by low-temperature field theories. These results are obtained following some heuristic assumptions on the character of stringy modifications to the gravitational 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 turn out to be borderline cases from several points of view. For lower dimensional world-volumes, a fully holographic behaviour is exhibited to order 1/N^2, and open strings in their presence are found to have a thermodynamical Hagedorn behaviour similar to that of closed strings in flat space.