Quantum gravity, the Planck lattice and the Standard Model

TL;DR

This paper explores a quantum gravity model using a Planck-scale lattice, proposing a Higgs-less mass generation mechanism for fermions and gauge bosons consistent with observations.

Contribution

It introduces a lattice-based approach to quantum gravity that extends the Standard Model without Higgs particles, addressing the Nielsen-Ninomiya no-go theorem.

Findings

A Higgs-less mass generation mechanism aligns with experimental data.

The model incorporates Nambu-Jona Lasinio terms to extend the Standard Model.

The Planck lattice provides a discrete structure for quantum gravity analysis.

Abstract

A possible ground state of Quantum Gravity is Wheeler's ``space-time foam'', which can be modeled as a ``Planck-lattice'', a space-time cubic lattice of lattice constant $a_P\simeq 10^{33}$cm, the Planck length. I analyse the structure of the Standard Model defined on the Planck Lattice, in the light of the ``no-go'' theorem of Nielsen and Ninomiya, which requires an extension of the continuum model through Nambu-Jona Lasinio terms, quadrilinear in the Fermi-fields. As a result, a theory of masses (of both fermions and gauge bosons) is seen to emerge that, without Higgs excitations, agrees well with observations.