Symmetries and Anomalies in the Continuum and on the Lattice

Based on joint work with Meng Cheng (arXiv:2211.12543), we will discuss some aspects of global symmetries and their ‘t Hooft anomalies.

We will define a notion of an emanant global symmetry. It is not a symmetry of the UV theory, but unlike emergent (accidental) symmetries, it is not violated by any relevant or irrelevant operators in the IR theory.

We will present lattice models with anomalous internal symmetries and see how the anomalies are diagnosed on the lattice using topological defects.

We will also discuss lattice models with anomalous lattice translation and relate them to an anomalous emanant symmetry in the IR theory. This will connect our discussion to the well-known Lieb-Schultz-Mattis theorem and to filling constraints like Luttinger theorem.