Anton Kapustin, Caltech
Anomalies and symmetry protected phases of matter
Topological Quantum Field Theory (TQFT) can be fruitfully applied to the
study of gapped phases of quantum matter. I will discuss how it can be
used to classify and understand properties of short-range entangled phases
of interacting bosonic matter with symmetries. The classification turns
out to be expressed in terms of Thom bordism groups. I will also explain
how TQFT can be used to understand anomalies for finite group symmetries.
Recently it was noted that symmetry in d-dimensional QFT is described by
a d-group rather than a group. I will explain how d-groups for d>1
naturally arise in the study of anomalies as well as the study of
fermionic phases of matter.