All-fermion electrodynamics and fermion number anomaly inflow

TL;DR

This paper shows that a 3+1D all-fermion electrodynamics system with fermionic charges and monopoles can only exist as the boundary of a 4+1D gapped, short-range entangled state, revealing a new fermion number anomaly.

Contribution

It provides evidence that all-fermion electrodynamics cannot be realized in isolation and must be viewed as a boundary phenomenon of a higher-dimensional topological state.

Findings

Demonstrates the boundary nature of all-fermion electrodynamics.

Identifies a novel fermion number anomaly.

Shows the bulk state is non-trivial and cannot be smoothly connected to a trivial product state.

Abstract

We demonstrate that 3+1-dimensional quantum electrodynamics with fermionic charges, fermionic monopoles, and fermionic dyons arises at the edge of a 4+1-dimensional gapped state with short-range entanglement. This state cannot be adiabatically connected to a product state, even in the absence of any symmetry. This provides independent evidence for the obstruction found by arXiv:1306.3238 to a 3+1-dimensional short-distance completion of all-fermion electrodynamics. The non-triviality of the bulk is demonstrated by a novel fermion number anomaly.