Final Report Summary - ADS-CFT-SOLVABLE (Origins of integrability in AdS/CFT correspondence)
This ERC project dealt with the fundamental properties of gauge (Yang-Mills) Quantum Field Theories - the main building block for the modern description of elementary particles and their interactions in the Nature. Those theories are very hard to study: most of the results we currently know on them concern the weakly interacting quantum fields, usually studied by Feynman perturbation theory. The maximally super-symmetric Yang-Mills theory in 4 dimensions N=4 SYM) is a rear example of such theories which can be studied for strongly interacting regime, by the famous AdS/CFT correspondence of J.Maldacena or even at all couplings, by exact quantum intractability methods worked out in the last 15 year, including my contributions. In this ERC project, I formulated with my collaborators the now widely known, and used in numerous works of researchers around the world, method of Quantum Spectral Curve (QSC). This method computes, at any interaction strength, exactly, at least in a special. planar 'tHooft limit, the spectrum of anomalous dimensions of N=4 SYM - the most important characteristics of this conformal field theory (CFT), mesuring the decay rate of correlation functions of various physical quantities. Another fundamental result of my ERC project is the formulation of a specific double scaling limit of this theory, resulting in the discovery of a new class of integrable four-dimensional strongly interacting non-unitary CFTs. It opened a vast research field of non-perturbative study of general properties of four- or even D-dimensional CFTs by quantum integrability methods. It also gives a clear insight into the origins of mysterious integrability properties of N=4 SYM - the main topic of the project, relating them to the non-compact 1+1-dimensional integrable quantum spin chains. We believe that our results give a unique opportunity of a general insight into the intimate properties of non-supersymmetric conformal field theories in physical space-time dimensions, and the results already obtained confirm our optimism.