A Cubic Matrix Action for the Standard Model and Beyond

TL;DR

This paper introduces a novel matrix theory framework that encodes field theories on toroidal spacetime using infinite Toeplitz matrices, enabling a unified cubic matrix action for the Standard Model and its extensions.

Contribution

It develops a new matrix-based approach to represent field theories, reconstructs the Standard Model within this framework, and explores its potential extensions.

Findings

Matrix theories equivalent to field theories on toroidal spacetime

Reconstruction of the Standard Model action in matrix form

Unified cubic matrix action encompassing Standard Model and beyond

Abstract

We propose a new framework for matrix theories that are equivalent to field theories on a toroidal spacetime. The correspondence is accomplished via infinite Toeplitz matrices whose entries match the field degrees of freedom on an energy-momentum lattice, thereby replacing the background geometry with matrix indices. These matrix theories can then be embedded into the purely cubic action of a single matrix and combined into a common universality class. We reconstruct the Standard Model action in this framework and discuss its extensions within the same class.