Integrability and the AdS/CFT correspondence

Didina Serban

IPhT

Fri, May. 29th 2009, 14:30

Amphi Claude Bloch, Bât. 774, Orme des Merisiers

The description of gauge theories at strong coupling is one of the long-standing problems in theoretical physics. The idea of a relation between strongly coupled gauge theories and string theory was pioneered by 't Hooft, Wilson and Polyakov. A decade ago, Maldacena made this relation explicit by conjecturing the exact equivalence of a conformally invariant theory in four dimensions, the maximally supersymmetric Yang-Mills theory, with string theory in the AdS5 x S5 background.
Other examples of the correspondence between a conformally invariant theory and string theory in an AdS background were discovered recently.
The comparison of the two sides of the correspondence requires the use of non-perturbative methods. The discovery of integrable structures in gauge theory by Minahan and Zarembo, and in string theory by Bena, Polchinski and Roiban, led to the conjecture that the two theories are integrable for any value of the coupling constant and that they share the same integrable structure defined non-perturbatively. The last seven years brought remarkable progress in identifying this solvable model and in explicitly solving the problem of computing the spectrum of conformal dimensions of the theory. The progress came from the identification of the dilatation operator with an integrable spin chain and from the study of the string sigma model. More progress is expected in the future from the thermodynamic Bethe ansatz approach for the sigma model and from the study of the dual conformal symmetry and its link with the remarkable properties of the gluon amplitudes.

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