IAS CMP/QFT Group Meeting
Some Topological Aspects of Quantum Field Theory in the Continuum and on the Lattice
Abstract: We will review the continuum c=1 conformal field theory and its lattice description in terms of a modified Villain model. Then, we will discuss its c=2 version. In addition to its standard zero-form internal symmetries, the model also has a -1-form symmetry associated with its theta-parameter. These symmetries combine to form a higher group with anomalies. When theta winds linearly around space, the internal symmetry group is violated, mixes with spatial translations, and becomes non-Abelian. Also, it leads to a non-invertible translation symmetry. We will then consider a lattice version of this system, using its modified Villain formulation. Surprisingly, all the subtleties in the symmetries of the continuum model exist on a finite lattice. This talk will be based on several papers, including 2406.06698, 2412.14434, and recent work with Yichul Choi, Sahand Seifnashri, and Wucheng Zhang, 2610.22485.