A second installment of a very successful forum with the same name held last year at Perimeter, this workshop will be devoted to conformal field theories (CFT), and in particular to the circle of ideas surrounding the conformal bootstrap program in three and four dimensions. The bootstrap has been fully successful for two-dimensional CFTs, but very little has been achieved in d >2. In view of recent advances, the time is ripe to reconsider the higher-dimensional bootstrap.

One physical motivation for studying the four-dimensional conformal theories is to learn more about Gauge theories such as QCD. Four-dimensional CFTs also often pop up in various scenarios of physics beyond the Standard Model, meant to solve puzzles related to flavor physics, the hierarchy problem, etc. Three-dimensional CFTs describe the critical behavior of condensed matter systems and holographically define quantum gravity in four dimensions.

In recent years, spectacular progress has been achieved towards the exact solution of some three- and four-dimensional CFTs, thanks to the AdS/CFT correspondence and to the application of integrability techniques. The best known examples are N=4 SYM in d=4 and the ABJM theory in d=3, for which the exact spectrum is largely understood. A complete solution of these theories will be a major breakthrough in theoretical physics. Given the spectrum, it is very natural to ask what are the constraints of crossing symmetry on higher-point functions.

The question can also be asked holographically, and we intend to discuss higher-point correlation functions in AdS/CFT. In particular, representations via Mellin-type integrals recently led to efficient recursion relation techniques for computing Witten diagrams. We would like to see if similar representations exist for the general conformal blocks, which take the role of Witten diagrams away from the large N limit.

An independent, but clearly related, line of research that has had notable recent success is the study of general bounds in CFTs that follow from crossing symmetry and unitarity. This method can also be applied to important models which are not known to be integrable, such as the 3D Ising model.

Finally, we would like to see if recent insights about RG flows connecting UV and IR conformal fixed points, like the proof of the a-theorem in 4-dimensions and the F-conjecture in 3-dimensions, can be put to use in the context of the bootstrap. A possible connection with the ongoing studies of the entanglement entropy is also interesting to explore.

The goal of this workshop is to bring together people working in these different approaches. The main theme is the higher-dimensional bootstrap program which is coming back to life.