Relating quantum field and gravity theories
Juan Maldacena proposed in 1997 a duality between superstring theory in the AdS background space and quantum field theories in four dimensions. This so-called anti-de Sitter/conformal field theory (AdS/CFT) correspondence is one of the most significant results in string theory. This relationship still has no formal mathematical proof, but in certain limits calculations are vastly simplified. Extensive checks carried out within the EU-funded project 'Spectrum of the planar AdS/CFT correspondence' (SPECTRUM OF ADS/CFT) involved calculations of observable quantities related by a specific dictionary – the dictionary that translates between the two theories. The energies of strings in the AdS5xS5space were conjectured by Maldacena to correspond to scaling dimensions of the 4D super Yang-Mills gauge theory (CFT4). Recently, these quantities were proposed to be solutions to certain set of equations. These equations follow from the Thermodynamic Bethe Ansatz, which is well-known in the field of integrable models. Integrable models are many-body systems that can be reduced to a combination of two-body systems rendering the equations solvable. SPECTRUM OF ADS/CFT scientists put this set of spectral equations to non-perturbative tests. The underlying idea is to look at the Thermodynamic Bethe Ansatz equations for excited states given a dynamic background. Such a background for the AdS5/CFT4 correspondence is furnished by the Gubser, Klebanov and Polyakov (GKP) solution. Next, a considerable amount of research was devoted to generalising this methodology to theories with less supersymmetry, such as AdS4/CFT3 and AdS3/CFT2.SPECTRUM OF ADS/CFT scientists gathered evidence in favour of these conjectured correspondences, as both theories of these dualities were shown to be solvable. A better understanding was offered on how physical quantities in each theory should be matched. These ideas of duality explored within the SPECTRUM OF ADS/CFT project have also been applied to low-energy systems, such as superconductors. The hope is that such dualities can soon be tested experimentally in laboratories, with exciting implications for other areas of condensed matter physics.
Keywords
Quantum field, gravity, condensed matter, AdS/CFT, string theory