A new web of dualities from Majorana Fermions

TL;DR

This paper introduces new dualities in 2+1D quantum field theories involving Majorana fermions, expanding the web of known dualities and providing insights into their infrared behavior and boundary conditions.

Contribution

It develops a hierarchy of bosonic dualities from Majorana fermions, including novel boson-boson dualities and boundary condition analyses, extending the 3D duality web.

Findings

Derived a hierarchy of dual bosonic descriptions from Majorana fermions.

Established explicit boson-boson dualities, such as $SO(N)$ with scalars and $U(1)$ with complex scalars.

Analyzed boundary conditions and their role in anomaly matching and central charges.

Abstract

We explore new infrared dualities in $(2+1)$-dimensional quantum field theories involving Majorana fermions. Building on the recently proposed operator-deformation approach to bosonization dualities, we incorporate the bosonization of neutral fermions into the established web of Dirac dualities. Starting from the decomposition of a Dirac fermion into two Majorana components, we derive a hierarchy of dual bosonic descriptions based on orthogonal Chern-Simons-matter theories. This construction leads to novel boson-boson dualities, including an explicit correspondence between an $SO(N)$ theory with two real scalars and a $U(1)$ theory with one complex scalar, and their generalizations to arbitrary numbers of Majorana flavours. We analyze boundary conditions preserving chirality and demonstrate their role in matching gravitational anomalies and chiral central charges. Additional deformations yield orthogonal analogues of Ising-Gross-Neveu and pairing transitions. The resulting framework provides a unified Majorana-based extension of the three-dimensional duality web and clarifies the infrared structure of non-Abelian bosonization.