Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D

Understand

In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group $G_f$ of the ground state splits as $G_f = G_b \times \mathbb{Z}_2^f$, where $\mathbb{Z}_2^f$ is generated by fermion parity, $(-1)^F$.

• In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when $G_f$ is not of the form $G_b \times \mathbb{Z}_2^f$.
• In this paper we study how $G_f$ together with the chiral central charge $c_-$ strongly constrain the existence of unpaired MZMs and the quantum numbers of symmetry defects.
• Our results utilize a recent algebraic characterization of (2+1)D invertible fermionic topological states, which provides a non-perturbative approach based on topological quantum field theory, beyond free fermions.