Physics Main Calendar

Abstract: The continuum limit is a standard tool in condensed-matter physics for deriving field theory descriptions of crystalline systems. However, a precise, model-independent framework for formulating this limit across all crystalline phases has been lacking. Gapped phases are a principal setting for this question: their universal low-energy behavior is captured by topological quantum field theories (TQFTs). Providing a mathematically precise continuum-limit construction for TQFTs therefore yields a rigorous statement about the universal, low-energy physics of gapped phases. In my talk, I will construct a single lattice object, functorially assembled from all finite point-group substructures that records exactly the crystalline data compatible with a continuum description. Focusing on invertible bosonic phases, I will then define a canonical map from this aggregate crystalline object to the continuum TQFT classification and outline why this map is surjective. Two consequences follow: the map is generally many-to-one, so distinct lattice phases can share a continuum image and some microscopic topological features are lost; and every continuum invertible TQFT in this class admits at least one faithful crystalline realization.