The last twenty years have witnessed extraordinary and continuing progress in our understanding of quantum many-body systems. This includes the discovery of new families of quantum phases of matter, and new kinds of critical phenomena at quantum phase transitions. A key underlying theme is the power of effective quantum field theories to describe universal properties of quantum systems, via a well-established paradigm developed over many years.
Today, this paradigm is being challenged by a new class of quantum systems known as fracton matter, defined by the presence of point-like excitations of restricted mobility. In this talk, I will introduce fracton systems and some of their surprising properties. I will also discuss why it has been challenging to build a general theory of fracton phases of matter; in particular, I will explain why the role of continuum quantum field theory in understanding fracton systems remains unclear.