Slava Rychkov (Université Paris 6, Ecole Normale Supérieure, CERN) - Jeudi 27 mars.
Renormalization group (RG) and Conformal Field Theory (CFT) are two complementary approaches to the theory of critical phenomena. The RG explains the underlying physical picture and allows approximate computations of the critical exponents, while CFT has been very efficient in solving models exactly. Until recently CFT was applied mostly in d=2, where the conformal group is infinite dimensional. Is there anything to gain from conformal symmetry in the three dimensional case ? We will argue that yes, both conceptually and quantitatively. Our particular example will be the critical point of the 3d Ising model. When viewed as a conformal field theory, it turns out to exhibit highly unusual properties, altogether unsuspected from the RG point of view. While the full theoretical significance of these results is not yet uncovered, they already led to the world-record determinations for the main critical exponents of the 3d Ising model.