A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
Arun Debray (Department of Mathematics, Purdue University, 150 N University Street, West Lafayette, IN, 47907, USA)
; Sanath Devalapurkar (Harvard University Department of Mathematics, 1 Oxford Street, Cambridge, MA, 02138, USA); Cameron Krulewski (Massachusetts Institute of Technology, Department of Mathematics, Simons Building, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA); Yu Liu (Harvard University Department of Mathematics, 1 Oxford Street, Cambridge, MA, 02138, USA); Natalia Pacheco-Tallaj (Massachusetts Institute of Technology, Department of Mathematics, Simons Building, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA); et al - Show all 6 authors
We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects, and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES). The mathematical backbone of the SBLES is studied in a companion paper [1]. Our work further develops the theory of higher Berry phase and its bulk-boundary correspondence, and serves as a new computational tool for classifying symmetry protected topological phases.
