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arXiv:1611.05049 · Physical review. B./Physical review. B

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

Max A. Metlitski, Ashvin Vishwanath, Cenke Xu

Published May 23, 2017• 58 citations
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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 $\mathrm{SO}{(N)}_{1}$ Chern-Simons gauge theory with a critical $\mathrm{SO}(N)$ vector bosonic matter field ($N\ensuremath{\ge}3$). The monopole of the $\mathrm{SO}(N)$ 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.

DOI
10.1103/physrevb.95.205137

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We construct a dual-bosonized description of a massless Majorana fermion in (2+1)ddd. 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\mathrm{SO}{(N)}_{1}SO(N)1​ Chern-Simons gauge theory with a critical SO(N)\mathrm{SO}(N)SO(N) vector bosonic matter field (N\ensuremath≥3N\ensuremath{\ge}3N\ensuremath≥3). The monopole of the SO(N)\mathrm{SO}(N)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 Nf{N}_{f}Nf​ flavors of Majorana fermions, and discuss possible resolutions of a caveat associated with an emergent global Z2{Z}_{2}Z2​ symmetry. Finally, we conjecture a dual description of an N=1\mathcal{N}=1N=1 supersymmetric fixed point in (2+1)ddd, which is realized by tuning a single flavor of Majorana fermions to an interacting (Gross-Neveu) critical point.
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