Orateur
James Drummond
(LAPTh & CERN)
Description
Nowadays, the notion of integrability is also used in string theories. The celebrated AdS / CFT correspondence conjecture between conformal field theories in four dimensions and string theory in a 11 dimensional space entered a predictive phase, following a tremendous breakthrough made in recent years. This conjecture predicts equivalence between operators in conformal field theories (eg N = 4 SYM) on the one hand, and the excited states of a superstring propagating on a curved anti-de Sitter spacetime on the other hand. Originally, the AdS / CFT correspondence applied to quasi-classical strings (relatively well studied) and conformal field theory in the strong coupling regime, virtually inaccessible by current methods. Most recently, this situation has completely changed after the discovery that the two theories are probably based on very similar integrability principles: integrable systems of Heisenberg spin chain type were found in the N = 4 SYM theory and also on the side of the quasi-classical string. This allowed for the first time, to compare (with success) quantitative predictions (and not merely qualitative, as early in the AdS / CFT) of string theory and perturbative results in conformal field theories. Together with this integrability appoach appeared infinite dimensional symmetry algebras, such as Yangians of superalgebras. These quantum groups encompass the superconformal symmetry algebra and allow to put severe constraints on the possible form of e.g. Wilson loops.
