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Center for Nonlinear Studies |
I will demonstrate, on a few examples of very different physical systems, how efficient can be the concept of integrability for obtaining non-trivial, exact and often rather explicit analytical results. A list of applications, still very limited, runs from electrons in 1+1 dimensional crystals and statistical mechanics on planar random lattices, to 1+1 dimensional quantum gravity, quantum field theory and string theory. One of the most spectacular achievements of the last few years is the exact solution for spectrum of anomalous dimensions of physical operators in the 3+1 dimensional Yang-Mills theory with N=4 supersymmetries. The so called AdS/CFT correspondence hypothesis allows to reformulate the 4-dimensional N=4 SYM theory as an integrable 1+1-dimensional quantum field theory, solvable by the known techniques of integrability, such as thermodynamical Bethe ansatz and integrable classical discrete Hirota dynamics. We will stress the common mathematical structure of all known, classical or quantum, integrable systems.
Host: Razvan Teodorescu