Topological gauge theory, symmetry fractionalization, and classification of symmetry-enriched topological phases in three dimensions

Symmetry plays a crucial role in enriching topological phases of matter. Phases with intrinsic topological order that are symmetric are called symmetry-enriched topological phases (SET). In this paper, we focus on SETs in three spatial dimensions, where the intrinsic topological orders are described by Abelian gauge theory and the symmetry groups are also Abelian. As a series work of our previous research [Phys. Rev. B 94, 245120 (2016); (arXiv:1609.00985)], we study these topological phases described by twisted gauge theories with global symmetry and consider all possible topologically inequivalent "charge matrices". Within each equivalence class, there is a unique pattern of symmetry fractionalization on both point-like and string-like topological excitations. In this way, we classify Abelian topological order enriched by Abelian symmetry within our field-theoretic approach. To illustrate, we concretely calculate many representative examples of SETs and discuss future directions

N′-Diphenyl­methyl­ene-2-hydroxy­benzohydrazide

The title compound, C20H16N2O2, was synthesized by the reaction of 2-hydroxy­benzohydrazide with diphenyl­methanone. The dihedral angle between the phenyl rings is 76.28 (11)°. The amino H atom is involved in an intra­molecular N—H⋯O hydrogen bond. In the crystal structure, the hydr­oxy groups and carbonyl O atoms form inter­molecular O—H⋯O hydrogen bonds, which link the mol­ecules into chains running along the b axis