# IQIM Postdoctoral and Graduate Student Seminar

*,*Cecil and Ida Green Professor of Physics

*,*Massachusetts Institute of Technology

*,*

**Abstract:** Global symmetry (0-symmetry) acts on the whole space while higher k-symmetry acts on the codimension-k subspaces. The usual condensed matter lattice theories do not have higher symmetries (unless we engineer fine-tuned toy models). However, for gapped systems, higher symmetries can emerge from the usual condensed matter theories at low energies (usually in a spontaneously broken form). We pointed out that the emergent spontaneously broken higher symmetries are nothing but a kind of topological orders. Thus the study of emergent spontaneously broken higher symmetries is a study of topological order. The emergent higher symmetries can be used to constrain possible phase transitions and possible phases induced by certain types of excitations in topological orders.

- This week only, the IQIM Seminar will be in 201 E. Bridge with lunch provided following the talk in 114 E. Bridge.