Constraining Conformal Field Theories

The Knut and Alice Wallenberg Foundation promoted on December 1, 2016 two new Academy Fellows to the Department of Physics and Astronomy, Karin Schönning and Agnese Bissi.

Conformal field theories (CFTs) are ubiquitous in theoretical physics. They play an important role in the classification of second order phase transitions, in the study of generic quantum field theories and in the AdS/CFT correspondence which connects quantum gravity in AdS and conformal field theories. All the dynamical information of CFTs is encoded in the dimensions and the three point functions of primary operators. It is actually possible to classify unitary CFTs using only symmetries. This is the essence of conformal bootstrap which states that any collection of dimensions and three point functions satisfying associativity of the operator product expansion (OPE) for all four point functions defines a consistent CFT. Nowadays one can systematically use this consistency relation to find numerical upper bounds for the dimension and the three point function of the lowest dimension primary operator appearing in the OPE of two operators with a given dimension. One of the major success is the study of the three dimensional Ising model at criticality. Since for this model the bound is actually saturated, it is possible to determine the dimension of the lowest dimensional operator, with the highest available accuracy. This program has also been successfully extended to superconformal field theories. From this viewpoint the peculiarity of these theories is the presence of operators whose dimensions and three point functions do not acquire any quantum correction. My proposal is to extend the conformal bootstrap program twofold: -extending the study of the superconformal theories by considering four point functions of non protected operators; -considering the conformal bootstrap program for non relativistic conformal field theories, which describe some condensed matter systems as cold atoms. Both extensions will help in understanding structural properties and behaviour of CFTs which are important in high energy physics as well as for condensed matter systems.