The Schr\"odinger functional in lattice QCD with exact chiral symmetry

TL;DR

This paper proposes a lattice formulation of the QCD Schr"odinger functional using the Neuberger-Dirac operator, ensuring key properties for numerical simulations in lattice QCD with exact chiral symmetry.

Contribution

It introduces a new lattice approach for the Schr"odinger functional in QCD that maintains exact chiral symmetry and satisfies essential physical and mathematical properties.

Findings

Formulation satisfies locality, symmetries, and hermiticity

Suitable for numerical lattice QCD simulations

Maintains exact chiral symmetry with Neuberger-Dirac operator

Abstract

Similarly to the interaction lagrangian, the possible boundary conditions in quantum field theories on space-time manifolds with boundaries are strongly constrained by the symmetry and scaling properties of the theory. Based on this general insight, a lattice formulation of the QCD Schr\"odinger functional is proposed for the case where the lattice Dirac operator in the bulk of the lattice coincides with the Neuberger--Dirac operator. The construction satisfies all basic requirements (locality, symmetries, hermiticity) and is suitable for numerical simulations.