Editing AdS/CFT correspondence (section)

== Applications to quantum field theory ==

=== Nuclear physics ===

{{Main|AdS/QCD}}

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 accelerator]]s. This state of matter arises for brief instants when heavy [[ions]] such as [[gold]] or [[lead]] [[Atomic nucleus|nuclei]] are collided at high energies. Such collisions cause the [[quarks]] that make up atomic nuclei to [[deconfinement|deconfine]] at temperatures of approximately two [[1,000,000,000,000|trillion]] [[kelvin]]s, conditions similar to those present at around 10<sup>−11</sup>&nbsp;seconds after the [[Big Bang]].{{sfn|ps=|Zwiebach|2009|p=559}}

The physics of the quark–gluon plasma is governed by quantum chromodynamics, but this theory is mathematically intractable in problems involving the quark–gluon plasma.{{refn|More precisely, one cannot apply the methods of perturbative quantum field theory.}} In an article appearing in 2005, [[Đàm Thanh Sơn]] and his collaborators showed that the AdS/CFT correspondence could be used to understand some aspects of the quark–gluon plasma by describing it in the language of string theory.{{sfn|ps=|Merali|2011|p=303}}{{sfn|ps=|Kovtun|Son|Starinets|2005}} By applying the AdS/CFT correspondence, Sơn and his collaborators were able to describe the quark gluon plasma in terms of black holes in five-dimensional spacetime. The calculation showed that the ratio of two quantities associated with the quark–gluon plasma, the [[shear viscosity]] ''η'' and volume density of [[entropy]] ''s'', should be approximately equal to a certain [[universal constant]]:
: <math>\frac{\eta}{s}\approx\frac{\hbar}{4\pi k}</math>
where ''ħ'' denotes the [[reduced Planck constant]] and ''k'' is the [[Boltzmann constant]].{{sfn|ps=|Zwiebach|2009|p=561}}{{sfn|ps=|Kovtun|Son|Starinets|2005}} In addition, the authors conjectured that this universal constant provides a [[lower bound]] for ''η''/''s'' in a large class of systems. In an experiment conducted at the [[Relativistic Heavy Ion Collider]] at [[Brookhaven National Laboratory]],  the experimental result in one model was close to this universal constant but it was not the case in another model.{{sfn|ps=|Luzum|Romatschke|2008|loc=Part IV. C}}

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 [[femtometre]]s. This phenomenon is characterized by a number {{overset|lh=0.3|^|''q''}} called the [[jet quenching]] parameter, which relates the energy loss of such a quark to the squared distance traveled through the plasma. Calculations based on the AdS/CFT correspondence give the estimated value {{nowrap|{{overset|lh=0.3|^|''q''}} ≈ {{val|4|u=GeV<sup>2</sup>/fm}}}}, and the experimental value of {{overset|lh=0.3|^|''q''}} lies in the range {{val|5|-|15|u=GeV<sup>2</sup>/fm}}.{{sfn|ps=|Zwiebach|2009|p=561}}

=== Condensed matter physics ===

[[File:Meissner effect p1390048.jpg|thumb|A [[magnet]] [[Meissner effect|levitating]] above a [[high-temperature superconductor]]. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.{{sfn|ps=|Merali|2011}}]]

{{Main|AdS/CMT}}

Over the decades, [[experimental physics|experimental]] [[condensed matter]] physicists have discovered a number of exotic states of matter, including [[superconductors]] and [[superfluids]]. These states are described using the formalism of quantum field theory, but some phenomena are difficult to explain using standard field theoretic techniques. Some condensed matter theorists including [[Subir Sachdev]] hope that the AdS/CFT correspondence will make it possible to describe these systems in the language of string theory and learn more about their behavior.{{sfn|ps=|Merali|2011|p=303}}

So far some success has been achieved in using string theory methods to describe the transition of a [[superfluid]] to an [[insulator (electricity)|insulator]]. A superfluid is a system of [[electrically neutral]] [[atoms]] that flows without any [[friction]]. Such systems are often produced in the laboratory using [[liquid helium]], but recently{{When|date=July 2021}} experimentalists have developed new ways of producing artificial superfluids by pouring trillions of cold atoms into a lattice of criss-crossing [[lasers]]. These atoms initially behave as a superfluid, but as experimentalists increase the intensity of the lasers, they become less mobile and then suddenly transition to an insulating state. During the transition, the atoms behave in an unusual way. For example, the atoms slow to a halt at a rate that depends on the [[temperature]] and on the Planck constant, the fundamental parameter of quantum mechanics, which does not enter into the description of the other [[phase (matter)|phases]]. This behavior has recently been understood by considering a dual description where properties of the fluid are described in terms of a higher dimensional black hole.{{sfn|ps=|Sachdev|2013|p=51}}

=== Criticism ===
With many physicists turning towards string-based methods to solve 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,{{sfn|ps=|McLerran|2007}} an American physicist, [[Larry McLerran]] pointed out that the {{nowrap|1=''N'' = 4}} super Yang–Mills theory that appears in the AdS/CFT correspondence differs significantly from quantum chromodynamics, making it difficult to apply these methods to nuclear physics. According to McLerran,

{{Blockquote|text=''N''&nbsp;=&nbsp;4 supersymmetric Yang–Mills is not QCD&nbsp;... It has no mass scale and is conformally invariant. It has no confinement and no running coupling constant. It is supersymmetric. It has no chiral symmetry breaking or mass generation. It has six scalar and fermions in the adjoint representation&nbsp;... It may be possible to correct some or all of the above problems, or, for various physical problems, some of the objections may not be relevant. As yet there is not consensus nor compelling arguments for the conjectured fixes or phenomena which would insure that the {{nowrap|1=''N'' = 4}} supersymmetric Yang Mills results would reliably reflect QCD.{{sfn|ps=|McLerran|2007}}}}

In a letter to [[Physics Today]], [[Nobel laureate]] [[Philip W. Anderson]] voiced similar concerns about applications of AdS/CFT to condensed matter physics, stating

{{Blockquote|text=As a very general problem with the AdS/CFT approach in condensed-matter theory, we can point to those telltale initials "CFT"—conformal field theory. Condensed-matter problems are, in general, neither relativistic nor conformal. Near a quantum critical point, both time and space may be scaling, but even there we still have a preferred coordinate system and, usually, a lattice. There is some evidence of other linear-T phases to the left of the strange metal about which they are welcome to speculate, but again in this case the condensed-matter problem is overdetermined by experimental facts.{{sfn|ps=|Anderson|2013}}}}