Horizon Condition Holds Pointwise on Finite Lattice with Free Boundary Conditions

TL;DR

This paper proves that the horizon condition, important in gauge theory, applies pointwise to all configurations on finite lattices with free boundary conditions, extending its known validity.

Contribution

It establishes the horizon condition's pointwise validity on finite lattices with free boundary conditions, a significant extension from previous continuum and periodic lattice results.

Findings

Horizon condition holds pointwise on finite lattices with free boundary conditions.

Validates the horizon condition for all transverse configurations on such lattices.

Extends the understanding of gauge theory conditions to finite lattice settings.

Abstract

It is proven that the "horizon condition", which was found to characterize the fundamental modular region in continuum theory and the thermodynamic limit of gauge theory on a periodic lattice, holds for every (transverse) configuration on a finite lattice with free boundary conditions.