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

Abstract

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 ($N\ge 3$). The monopole of the $SO(N)$ gauge field is identified with the Majorana fermion. We provide evidence for the duality by establishing the correspondence of adjacent gapped phases and by a parton construction. We also propose a generalization of the duality to $N_f$ flavors of Majorana fermions, and discuss possible resolutions of a caveat associated with an emergent global $Z_2$ symmetry. Finally, we conjecture a dual description of an $\mathcal{N}=1$ supersymmetric fixed point in $(2+1)d$, which is realized by tuning a single flavor of Majorana fermions to an interacting (Gross-Neveu) critical point.

11 pages

References in corpus (5)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Particle-Vortex Duality from 3d Bosonization
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Yukawa CFTs and Emergent Supersymmetry

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