Surface states and chiral symmetry on the lattice

TL;DR

This paper explores chiral symmetry and surface states in lattice fermions using a Hamiltonian approach, offering new methods for zero quark mass limits and illustrating anomalies through extra-dimensional state flows.

Contribution

It introduces a novel Hamiltonian formalism for lattice fermions with surface states, enabling natural zero quark mass limits and new perspectives on chiral anomalies and gauge coupling extensions.

Findings

Surface states bound to a wall in an extra dimension model chiral symmetry.

Flow of states in the extra dimension illustrates the chiral anomaly.

Proposes two methods for gauge coupling extension with different symmetry breaking mechanisms.

Abstract

In a Hamiltonian formalism we study chiral symmetry for lattice Fermions formulated in terms of Shockley surface states bound to a wall in an extra spatial dimension. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. We illustrate the chiral anomaly as a flow of states in this extra dimension. We discuss two alternatives for extending the picture to a chiral coupling of gauge fields to such Fermions; one with a small explicit breaking of gauge symmetry and one one with heavy mirror Fermions.