Adam Artymowicz
California Institute of Technology
Title
Lattice topological invariants from anomalies
Abstract
A long-term goal in modern physics is the classification of gapped phases of matter at zero temperature in the presence of an onsite symmetry. To do this, one looks for measurable quantities which act as invariants of the phase of matter. One example is the Hall conductance, which is an invariant of physical systems in 2 spatial dimensions in the presence of a U(1) symmetry. In this talk I will report on recent work with Anton Kapustin and Bowen Yang which concerns a general framework that produces invariants in every spatial dimension for any compact connected Lie group. We show that these invariants correspond to anomalies, which are topological obstructions to gauging (ie. promoting a global symmetry to a local one).
