Strongly interacting systems (SIS) are very common in Nature, famous examples ranging from the fundamental theory of quarks and gluons - Quantum Chromo-Dynamics (QCD) - to quantum critical systems, high-temperature superconductors, strange metals, quantum Hall systems and possibly even new materials as graphene. In these systems the interaction between different particles becomes so intense that the most common mathematical tools used to describe them break down and the traditional paradigms based on weakly interacting degrees of freedom cannot be applied.
A promising powerful technique to investigate SIS is the holographic correspondence, often referred to as AdS/CFT or gauge/gravity duality. It is founded on a duality map between ordinary quantum field theories (QFTs) and higher dimensional models of gravity and strings. |
The growing activity around the AdS/CFT paradigm has fostered the development of new techniques, mainly in the context of supersymmetric QFTs, to understand exact dynamics of quantum gauge theories.
Localization is one of these: the supersymmetry algebras can be sometimes deformed to accommodate background curvatures and the partition functions for the resulting quantum theories can be evaluated in closed form via a particular saddle-point procedure, known as the supersymmetric localization. Thanks to this method, a huge number of new exact results has been derived in different contexts, for local and non-local observables: the strong coupling limits have been compared with holographic predictions, supporting in general the validity of the duality. |
The duality has also benefited from all the tools provided by integrability. The latter is a fundamental ingredient for understanding the gravitational/string description of certain strongly interacting gauge theories. For instance, the sigma-models effectively describing their strong coupling regime are in some cases naturally endowed with an integrable structure. Quite surprisingly this property survives in the dual field theoretical picture and is used to obtain exact results at any coupling for quantities such as the spectrum of anomalous dimensions of operators in maximally supersymmetric QFTs!
Lately the correspondence has also led to unravel novel relations between observables, such as the connection between scattering amplitudes and Wilson loops superconformal gauge theories. |
Holography, QCD and dark matter
A typical problem one can address in this framework is the strong dynamics of hadronic matter. A first-principle approach is provided by a reformulation of QCD on Euclidean lattices and the use of numerical Monte Carlo methods. This technique, powerful when studying equilibrium properties, has still severe limitations when analyzing real-time dynamical issues or finite quark density regimes. Holography has already had some success in modelling the low viscosity fluid state of matter called Quark Gluon Plasma, which was created in heavy ion collision experiments at Brookhaven National Laboratory, and, more recently, at the LHC at CERN. Moreover in QFT models where additional symmetries are present (typically supersymmetries) exact dynamical properties of the strong coupling regime as confinement, chiral symmetry breaking and critical exponents have been derived by using gauge/gravity duality.
People working on this topics here: F. Bigazzi, A. Cotrone and D. Seminara Useful Reviews: arXiv:0709.1523 (A simple and classic review by D. Mateos). See also the book by M. Ammon and J. Erdmenger. |