Duality and bosonization of (2 + l)-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.