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Particle-vortex duality is a powerful theoretical tool that has been used tostudy bosonic systems. Here we propose an analogous duality for Dirac fermionsin 2+1 dimensions. The physics of a single Dirac cone is proposed to bedescribed by a dual theory, QED3 with a dual Dirac fermion coupled to a gaugefield. This duality is established by considering two alternate descriptions ofthe 3d topological insulator (TI) surface. The first description is the usualDirac cone surface state. The second description is accessed via anelectric-magnetic duality of the bulk TI coupled to a gauge field, which mapsit to a gauged topological superconductor. This alternate descriptionultimately leads to a new surface theory - dual QED3. The dual theory providesan explicit derivation of the T-Pfaffian state, a proposed surface topologicalorder of the TI, which is simply the paired superfluid state of the dualfermions. The roles of time reversal and particle-hole symmetry are exchangedby the duality, which connects some of our results to a recent conjecture bySon on particle-hole symmetric quantum Hall states.

Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators