Abstract: | Composite Dirac liquids: parent states for symmetric surface topological order We introduce exotic gapless states `composite Dirac liquids' that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that preserve all symmetries yet retain thermal properties similar to those of the non-interacting topological insulator surface. Composite Dirac liquids form an ideal starting point for understanding fully gapped, topologically ordered surface states of topological insulators, such as the T-Pfaffian. |