The Standard Model in the Latticized Bulk

TL;DR

This work develops a manifestly gauge-invariant $3+1$-D effective Lagrangian describing the Standard Model in a $4+1$ bulk via the transverse lattice. It treats QCD and electroweak sectors with replicated gauge groups linked by scalar fields, and analyzes two Higgs configurations—universal and localized—alongside a split-generation fermion setup. The study derives KK-like spectra for gauge bosons and Higgs sectors, showing that a localized or universal Higgs yields the usual SM masses with volume-suppressed quartics, but extra dimensions do not resolve the electroweak naturalness problem. The framework provides a renormalizable, gauge-invariant description that connects extra-dimensional intuition with a purely $3+1$-D model, offering pathways for extensions to SUSY, gravity, and flavor physics while highlighting challenges such as FCNCs and anomaly considerations.

Abstract

We construct the manifestly gauge invariant effective Lagrangian in 3+1 dimensions describing the Standard Model in 4+1 dimensions, following the transverse lattice technique. We incorporate split generation fermions and we explore naturalness for two Higgs configurations: a universal Higgs VEV, common to each transverse brane, and a local Higgs VEV centered on a single brane with discrete exponential attenuation to other branes, emulating the split-generation model. Extra dimensions, with explicit Higgs, do not ameliorate the naturalness problem.