Fermionic SPT phases in higher dimensions and bosonization

Understand

We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with higher-form symmetries.

• We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry G.
• It generalizes the supercohomology of Gu and Wen.
• We argue that the most general such phase can be obtained from a bosonic "shadow" by condensing both fermionic particles and strings.