Light fermion masses in partially deconstructed models

TL;DR

This paper explores how to construct models with two extra dimensions using dimensional deconstruction, aiming to replicate various compactification geometries like tori, cylinders, and orbifolds in a discrete framework.

Contribution

It extends the dimensional deconstruction approach to two extra dimensions, modeling complex geometries and orbifolds in a discrete setting.

Findings

Models successfully mimic two-dimensional tori, cylinders, and rectangular regions.

Proposed models approximate continuum limits of extra-dimensional theories.

Framework can incorporate magnetic flux and orbifold structures.

Abstract

Considering a theory space consisting of a large number of five-dimensional Dirac fermion field theories including background abelian gauge fields, we can construct a theory similar to a continuous six-dimensional theory compactified with two-dimensional manifolds with and without magnetic flux or orbifolds as extra dimensions. This method, called dimensional deconstruction, can be used to construct a model with one-dimensional discrete space, which represents general graph structures. In this paper, we propose the models with two extra dimensions, which resemble two-dimensional tori, cylinders, and rectangular regions, as continuum limits. We also try to build a model that mimics one with the two-dimensional orbifold compactification.