Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED

TL;DR

This paper constructs staggered fermions for transverse lattice QED, analyzes perturbative finiteness, identifies a potential critical point for chiral symmetry breaking, and studies non-perturbative symmetry breaking in the strong coupling limit.

Contribution

It introduces a transverse lattice regularization for QED with staggered fermions and explores the phase transition related to chiral symmetry breaking.

Findings

Transverse lattice QED is perturbatively finite at fixed lattice spacing.

A critical coupling point for non-renormalizability and chiral symmetry breaking is identified.

Strong coupling analysis links the ground state to a 2D Heisenberg antiferromagnet.

Abstract

Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice non-compact QED is developed in light-cone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the interaction Hamiltonian becomes non-renormalizable for $g^2(a) > 4\pi$, where $g(a)$ is the bare (lattice) QED coupling constant. We conjecture that this is the critical point of the chiral symmetry breaking phase transition in QED. Non-perturbative chiral symmetry breaking is then studied in the strong coupling limit. The discrete remnant of chiral symmetry that remains on the lattice is spontaneously broken, and the ground state to lowest order in the strong coupling expansion corresponds to the classical ground state of the two-dimensional spin one-half Heisenberg antiferromagnet.