Emergent generalized symmetry and maximal symmetry-topological-order

Understand

A characteristic property of a gapless liquid state is its emergent symmetry and dual symmetry, associated with the conservation laws of symmetry charges and symmetry defects respectively.

• These conservation laws, considered on an equal footing, can't be described simply by the representation theory of a group (or a higher group).
• They are best described in terms of a topological order (TO) with gappable boundary in one higher dimension; we call this the symTO of the gapless state.
• The symTO can thus be considered a fingerprint of the gapless state.