Strong Coupling Qed Breaks Chiral Symmetry

TL;DR

This paper demonstrates that in the strong coupling limit, d-dimensional QED with multiple fermion flavors maps onto a quantum Heisenberg antiferromagnet, linking chiral symmetry breaking to magnetic order phases.

Contribution

It establishes a novel correspondence between strong coupling QED and quantum antiferromagnets, providing insights into chiral symmetry breaking mechanisms.

Findings

QED maps onto the Heisenberg antiferromagnet in strong coupling

Chiral symmetry breaking relates to magnetic phase transitions

Pions correspond to spin-wave excitations

Abstract

We show that the strong coupling limit of d-dimensional quantum electrodynamics with $2^{d}/2^{[d/2]}$ flavors of fermions can be mapped onto the s=1/2 quantum Heisenberg antiferromagnet in d-1 space dimensions. The staggered N\'eel order parameter is the expectation value of a mass operator in QED and the spin-waves are pions. We speculate that the chiral symmetry breaking phase transition corresponds to a transition between the flux phase and the conventional N\'eel ordered phase of an antiferromagnetic t-J model.