Duality and bosonization of (2+1)-dimensional Majorana fermions

摘要

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 >= 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 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.