Five-dimensional Lattice Gauge Theory as Multi-Layer World

Abstract

A five-dimensional lattice space can be decomposed into a number of four-dimens ional lattices called as layers. The five-dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. In the theory, there exist two independent coupling constants; $β_4$ controls the dynamics inside a layer and $β_5$ does the strength of the inter-layer interaction.We propose the new possibility to realize the continuum limit of a five-dimensional theory using four-dimensional dynamics with large $β_4$ and small $β_5$. Our result is also related to the higher dimensional theory by deconstruction approach.