Five-dimensional Lattice Gauge Theory as Multi-Layer World

TL;DR

This paper explores a five-dimensional lattice gauge theory decomposed into four-dimensional layers, proposing a new way to realize the continuum limit through specific coupling constants and relating it to higher-dimensional theories via deconstruction.

Contribution

It introduces a novel approach to achieve the continuum limit of five-dimensional theories using layered four-dimensional dynamics with distinct coupling constants.

Findings

Identification of two independent coupling constants $eta_4$ and $eta_5$

Proposal of a new continuum limit approach with large $eta_4$ and small $eta_5$

Connection to higher-dimensional theories through deconstruction

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; $\beta_4$ controls the dynamics inside a layer and $\beta_5$ 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 $\beta_4$ and small $\beta_5$. Our result is also related to the higher dimensional theory by deconstruction approach.