Comments on Lattice vs. Continuum Quantum Field Theory
Nathan Seiberg (IAS)
Abstract: There is an interesting interplay between continuum quantum field theory (QFT) and lattice systems. First, as in condensed-matter physics, we start at short distances (UV) with a lattice model and our goal is to find its long distance (IR) behavior. The lore is that this behavior is captured by a continuum QFT. Conversely, as is more common in high-energy physics and mathematical physics, the lattice theory is a first step toward a rigorous definition of the continuum theory. Despite enormous progress over the past decades, these two directions of the interplay between the lattice and the continuum face interesting challenges.
Here, motivated by recently discovered theoretical phases of matter (including the XY-plaquette model and models of fractons), we will address two aspects of the relation between the lattice in the UV and the continuum in the IR. We will present lattice models exhibiting topological properties of continuum theories, like winding symmetries, ‘t Hooft anomalies, and duality. We will use this approach to clarify the subsystem global symmetries of some of the recently discovered exotic models. We will also discuss some more dynamical aspects of these systems and in particular their enigmatic UV/IR mixing; i.e., some long-distance properties are sensitive to short-distance details.
differential geometrymetric geometry
Audience: researchers in the discipline
Western Hemisphere colloquium on geometry and physics
Series comments: Description: Biweekly colloquium of geometers and physicists
This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.
Organizer: | David R. Morrison* |
*contact for this listing |