Physics Club: Slava Rychkov, CERN, “The Conformal Bootstrap Approach to Criticality in 3 and 2+1 dimensions”

The nonperturbative conformal bootstrap has re-emerged in recent years as a powerful technique to compute properties of the critical state of matter. Starting from the key assumption - that the critical theory possesses conformal symmetry - and other experimentally justifiable assumptions like the internal symmetry group and the number of relevant (in the RG sense) couplings, the conformal bootstrap allows to find allowed regions in the parameter space of the CFT data. These constraints are universal - they should be satisfied by any microscopic theory satisfying the assumptions. For some universality classes like that of the 3d Ising model and the O(N) model the constraints are surprisingly sharp, for reasons which are as yet mysterious. They provide the world’s most precise determinations of the critical exponents and transport coefficients for these models. We will review the method, which has its roots in high energy physics, and the fruitful interplay now taking place with the condensed matter physics.