| We examine the thermodynamic behavior of a field theory resulting from a system of intersecting D3 branes, treating one brane as a probe in the Anti de Sitter--Schwarzschild geometry generated by the other branes. We examine the equation of state that is supposed to characterize the boundary field theory, and see that it exhibits features of both a local instability, at odds with the fluctuation-disspation theorem, and an unbounded free energy that gives a global instability. An effort to understand these apparent instabilities will lead to the study of a toy model that captures the important features of the brane system, and see that the apparent instabilities of the system are best described as UV divergences, that give rise to renormalization ambiguities. The degree of ambiguity introduced by renormalization will call into question the physicality of the equation of state, but as we will see, we will come to the conclusion that the infinite ambiguity is a reflection of ambiguity in the choice of order parameter, and not necessarily in the system itself. In addition, ultimately we will be able to make precise quantitative predictions about the critical thermodynamic behavior of the system, as a metastable state becomes unstable. The degree to which the conclusions we arrive at are applicable to other systems studied in AdS/CFT will also be discussed. |
