Collimated sprays of hadrons, called jets, are an emergent phenomenon of Quantum Chromodynamics (QCD) at high energies. Understanding the detailed energy flow, or substructure, of jets has come to play a central role at the Large Hadron Collider (LHC), where it has enabled new ways to search for physics beyond the Standard Model, as well as new insights into the strong interactions.
In this talk I will present recent developments in improving our theoretical understanding of jet substructure using insights from conformal field theory. I will show that jet substructure can be formulated as the study of matrix elements of particular lightray operators enabling the use of powerful techniques such as the operator product expansion (OPE), and providing an alternative approach to thinking about jet substructure more closely related to scaling phenomena. I will then show that the remarkable data quality of the LHC allows the scaling behavior predicted by the OPE to be directly measured in data, illustrating an interesting interplay between recent developments in CFT and LHC phenomenology.