Holographic correspondence confirms the properties of quark-gluon plasma

The study compared theoretical predictions with data from particle collisions carried out at the LHC and RHIC. Maldacena’s conjecture showed strong convergence with the experimental results.

By José Tadeu Arantes  |  Agência FAPESP – The “holographic correspondence,” also known as “AdS/CFT duality,” is a concept in theoretical physics that correlates gravity in a five-dimensional space (AdS) with a field theory in a four-dimensional space (CFT). In other words, it proposes describing gravity by means of a gravity-free field theory with one less dimension. This concept is easier to understand through an analogy: Imagine a spherical body. All the information about what happens in its three-dimensional core could be holographically encoded in the two-dimensional border surrounding it.

In 1997, Argentine physicist Juan Maldacena proposed this holographic correspondence as a conjecture. The aim was to solve the difficult equations of quantum gravity in five dimensions using the equations of particle theory in four dimensions. Maldacena, born in Buenos Aires in 1968, became the youngest tenured professor at Harvard University in the United States in 1999 and has held a chair at the Institute for Advanced Study in Princeton since 2001. His conjecture has been instrumental in addressing issues such as the entropy of black holes and the properties of quark-gluon plasma. It could also contribute to the development of a quantum theory of gravity.

Professor Roldão da Rocha, from the Federal University of ABC (UFABC) in the state of São Paulo, Brazil, used the Maldacena conjecture to investigate the relationship between the deformations of black branes and the shear viscosity of quark-gluon plasma. The results were published in The European Physical Journal Plus.

In the context of string theory and gravity in higher dimensions, it is important to note that black branes are generalizations of black holes. While conventional black holes are points or spheres in three-dimensional space, black branes are extended surfaces with extra dimensions. Like black holes, black branes have an event horizon, which defines the region beyond which nothing can escape. Another relevant fact is that, similar to the Hawking radiation of conventional black holes, black branes can emit thermal radiation.

Quark-gluon plasma (QGP) is a state of matter in which quarks and gluons, which are normally confined in hadrons (such as protons, neutrons, and mesons), move freely. This state existed in the moments following the Big Bang and can be recreated in heavy ion collisions, such as those produced by the Large Hadron Collider (LHC) in Europe and the Relativistic Heavy Ion Collider (RHIC) in the United States. QGP is a droplet approximately the size of a proton’s classical radius (a femtometer) that behaves like an almost perfect fluid. It exists for only 10⁻²³ seconds after production at a temperature of approximately 2 trillion kelvins.

“The study relied on a vast set of data provided by the LHC and RHIC. In the context of the AdS/CFT duality, five-dimensional gravity in a negatively curved space [Anti-de Sitter space, or AdS] can describe interactions of quark and gluon plasma in four dimensions using hydrodynamics. This approach enables the calculation of transport and response coefficients, such as shear viscosity, from gravitational solution perturbations. The holographic correspondence suggests that the black brane can be seen as a gravitational analog of plasma behavior. It can describe an almost perfect torrid fluid at the edge of AdS,” says Rocha.

The researcher demonstrated that the ratio of shear viscosity to entropy density of QGP, as measured experimentally, aligns remarkably well with the value calculated from quantum Schwarzschild black hole corrections in the AdS/CFT formalism. “This duality provides a dictionary between gravity and relativistic fluid mechanics. We can calculate quark and gluon plasma coefficients from the gravitational side and, at the same time, use fluid mechanics to better understand gravity,” he says.

The research also indicates that, while it is possible to deform the black brane geometry, experimental data impose strict limits. The deformation cannot exceed 1% of the original value dictated by the Schwarzschild black brane solution in AdS. “This suggests that the standard formulation of the AdS/CFT duality is extremely robust,” says Rocha.

One aspect of AdS/CFT duality that is often questioned is the introduction of an extra dimension in the gravitational formulation. Rocha argues that the fifth dimension should not be interpreted as a spatial dimension necessarily accessible experimentally but rather as an energy scale of quantum chromodynamics (QCD). “Duality does not mean that there’s a fifth dimension in the observable universe. It indicates that we can describe the plasma of quarks and gluons using a five-dimensional space as an effective mathematical resource,” he stresses.

This approach also has applications in other areas of physics, including condensed matter and holographic superconductors. The robustness and wide applicability of duality reinforce the relevance of holographic correspondence, even though it remains a conjecture rather than a consolidated theory. “From its proposition in 1997 until today, almost three decades later, Maldacena’s conjecture has been tested in various fields of physics and has done very well. Our study is further testimony to its robustness,” concludes Rocha.

The study was supported by FAPESP through the special project “Cherenkov Telescope Array: Construction and First Discoveries” and the Regular Research Grant “Holographic Gauge/Gravity Correspondences, Response and Transport Coefficients, and Quantum Corrections”. 

The article “Deformations of the AdS-Schwarzschild black brane and the shear viscosity of the quark-gluon plasma” is available at: link.springer.com/article/10.1140/epjp/s13360-024-05795-8.