Surface states and chiral symmetry on the lattice

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.

25 pages, BNL-60062

References in corpus (8)

• Chiral Fermions from Lattice Boundaries
• Chiral Fermions on the Lattice
• Evidence for the Role of Instantons in Hadron Structure from Lattice QCD
• Removing fermion doublers in chiral gauge theories on the lattice
• Investigation of the Domain Wall Fermion Approach to Chiral Gauge Theories on the Lattice
• Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass
• Perturbative analysis for Kaplan's lattice chiral fermions
• Anomaly through Gauge Invariant Regularization with Infinite Number of Pauli-Villars Fields

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