Title: Fermion-fermion duality in 3+1 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. In this talk, I present a generalisation of the Son’sfermion-fermion duality to 3+1 dimensions. I 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 gauge field coupled to the emergent and electromagnetic vector potentials. Firstly, I demonstrate the duality in the massive case. Secondly, I discuss the duality in the case of massless fermions starting from a lattice model and employing the slave-rotor approach already used in 2+1-dimensional systems. I finally apply this new duality to 3D Dirac semimetals in the low-energy regime. Besides their implications in topological phases of matter, these results shed light on the possible existence of a novel web of dualities in
3+1-dimensional (non-supersymmetric) quantum field theories.

Talk – PDF