In theoretical physics, the anti-de Sitter/quantum chromodynamics correspondence is a goal (not yet successfully accomplished) to describe quantum chromodynamics (QCD) in terms of a dual gravitational theory, following the principles of the AdS/CFT correspondence in a setup where the quantum field theory is not a conformal field theory.
The proposal of the AdS/CFT correspondence in late 1997 was the culmination of a long history of efforts to relate string theory to nuclear physics.[1] In fact, string theory was originally developed during the late 1960s and early 1970s as a theory of hadrons, the subatomic particles like the proton and neutron that are held together by the strong nuclear force. The idea was that each of these particles could be viewed as a different oscillation mode of a string. In the late 1960s, experimentalists had found that hadrons fall into families called Regge trajectories with squared energy proportional to angular momentum, and theorists showed that this relationship emerges naturally from the physics of a rotating relativistic string.[2]
On the other hand, attempts to model hadrons as strings faced serious problems. One problem was that string theory includes a massless spin-2 particle whereas no such particle appears in the physics of hadrons.[1] Such a particle would mediate a force with the properties of gravity. In 1974, Joël Scherk and John Schwarz suggested that string theory was therefore not a theory of nuclear physics as many theorists had thought but instead a theory of quantum gravity.[3] At the same time, it was realized that hadrons are actually made of quarks, and the string theory approach was abandoned in favor of quantum chromodynamics.[1]
In quantum chromodynamics, quarks have a kind of charge that comes in three varieties called colors. In a paper from 1974, Gerard 't Hooft studied the relationship between string theory and nuclear physics from another point of view by considering theories similar to quantum chromodynamics, where the number of colors is some arbitrary number
N
N
In late 1997, Juan Maldacena published a landmark paper that initiated the study of AdS/CFT. One special case of Maldacena's proposal says that N = 4 supersymmetric Yang–Mills theory, a gauge theory similar in some ways to quantum chromodynamics, is equivalent to string theory in five-dimensional anti-de Sitter space. This result helped clarify the earlier work of 't Hooft on the relationship between string theory and quantum chromodynamics, taking string theory back to its roots as a theory of nuclear physics.[5]
One physical system that has been studied using the AdS/CFT correspondence is the quark–gluon plasma, an exotic state of matter produced in particle accelerators. This state of matter arises for brief instants when heavy ions such as gold or lead nuclei are collided at high energies. Such collisions cause the quarks that make up atomic nuclei to deconfine at temperatures of approximately two trillion kelvins, conditions similar to those present at around
10-11
η
s
| η | ≈ | |
| s |
| \hbar | |
| 4\pik |
\hbar
k
η/s
Another important property of the quark–gluon plasma is that very high energy quarks moving through the plasma are stopped or "quenched" after traveling only a few femtometers. This phenomenon is characterized by a number
\widehat{q}
\widehat{q}
\widehat{q}
Despite many physicists turning towards string-based methods to attack problems in nuclear and condensed matter physics, some theorists working in these areas have expressed doubts about whether the AdS/CFT correspondence can provide the tools needed to realistically model real-world systems. In a talk at the Quark Matter conference in 2006,[12] Larry McLerran pointed out that the
N=4
\sqrt{sNN