Boson-Fermion Duality in Four Dimensions

In this talk, we propose a novel boson-fermion duality in four space-time dimensions by generalizing the lattice construction approach [1], which was applied to derive 3D boson-fermion duality [2]. Our analysis suggests that the Abelian Higgs model of θ=π is equivalent to a free Dirac fermion. The phase transition between topological and trivial insulators on the fermion side is dual to that between Higgs and confined phases on the boson side. Moreover, the Dirac fermion corresponds to a three-body bound state of one Higgs boson and two dyons in the bosonic theory.

[1] Takuya Furusawa and Yusuke Nishida, to appear.
[2] Jing-Yuan Chen, Jun Ho Son, Chao Wang, and S. Raghu, Phys. Rev. Lett. 120, 016602 (2018).