Duality and bosonization of (2+1)d Majorana fermions

Understand

We construct a dual bosonized description of a massless Majorana fermion in $(2+1)d$.

• In contrast to Dirac fermions, for which a bosonized description can be constructed using a flux attachment procedure, neutral Majorana fermions call for a different approach.
• We argue that the dual theory is an $SO(N)_1$ Chern-Simons gauge theory with a critical $SO(N)$ vector bosonic matter field ($N \geq 3$).
• The monopole of the $SO(N)$ gauge field is identified with the Majorana fermion.