String Theory Implications on Causal Hydrodynamics

Abstract

Causal hydrodynamics is one of the most active areas in the studies of quarkgluon plasma (QGP), and I will tell you the implications of string theory on this issue.1)–3) I first review the relation between QGP and string theory quickly in this section. Then, I explain the basic idea of causal hydrodynamics pedagogically in §2. Our aim is to study causal hydrodynamics from string theory which is described in §3. Actually, a number of papers appeared recently on this issue.4)–6),∗∗) In particular, our paper has many overlaps with Ref. 5). Our main tool is the so-called AdS/CFT duality.15) The AdS/CFT duality claims that a finite temperature gauge theory at strong coupling is dual to a black hole. A black hole appears since a black hole is a thermal system as well. Due to the Hawking radiation, a black hole has the notion of temperature: this is the reason why there can be a correspondence between these two in the first place. Since QGP is exactly a finite temperature gauge theory system at strong coupling, our aim is to study QGP using black holes. According to RHIC experiment, QGP behaves like a fluid with a very low viscosity. Then, the AdS/CFT duality implies that a black hole also behaves like a fluid with a low viscosity. In fact, black holes and hydrodynamic systems behave similarly (Fig. 1). For example, consider a water pond and drop some object. Then, you generate surface waves, but they decay quickly, and the water pond returns to a state of stable equilibrium. This is a dissipation phenomenon; in hydrodynamics, the dissipation is a consequence of viscosity. Black holes behave similarly. Again drop some object to a black hole. Then, the shape of the black hole horizon is distorted, but such a perturbation is not stable. It decays quickly, and the black hole returns to the original symmetric shape. If you regard this as a dissipation as well, the dissipation occurs in this case since the perturbation is absorbed by the black hole. Thus, you can consider the notion of viscosity for black holes as well, and the “viscosity” for black holes should be calculable from such a process.