# Fermion-fermion duality in 3+1 dimensions

## TL;DR

This paper extends fermion-fermion duality from 2+1 to 3+1 dimensions, revealing a new duality between charged and neutral fermions coupled to gauge fields, with implications for topological matter and quantum field theories.

## Contribution

It proposes a novel 3+1-dimensional fermion-fermion duality, generalizing previous 2+1-dimensional results, and demonstrates this duality in both massive and massless cases using lattice and field theory methods.

## Key findings

- Duality between charged Dirac fermions and neutral fermions with emergent gauge fields.
- Application of the duality to 3D Dirac semimetals.
- Insights into non-supersymmetric dualities in higher dimensions.

## Abstract

Dualities play a central role in both quantum field theories and condensed matter systems. Recently, a web of dualities has been discovered in 2+1 dimensions. Here, we propose in particular a generalization of the Son's fermion-fermion duality to 3+1 dimensions. We show that the action of charged Dirac fermions coupled to an external electromagnetic field is dual to an action of neutral fermions minimally coupled to an emergent vector gauge field. This dual action contains also a further tensor (Kalb-Ramond) gauge field coupled to the emergent and electromagnetic vector potentials. We firstly demonstrate the duality in the massive case. We then show the duality in the case of massless fermions starting from a lattice model and employing the slave-rotor approach already used in the 2+1-dimensional duality [Burkov, Phys. Rev. B 99, 035124 (2019)]. We finally apply this result to 3D Dirac semimetals in the low-energy regime. Besides the implications in topological phases of matter, our results shed light on the possible existence of a novel web of dualities in 3+1-dimensional (non-supersymmetric) quantum field theories.