Why the Standard Model

TL;DR

This paper proposes a purely gravitational, noncommutative geometric explanation for the Standard Model, reproducing its structure and particles through a novel space-time framework involving finite noncommutative geometries.

Contribution

It introduces a noncommutative geometric model that reproduces the Standard Model's gauge structure and particle content from a gravitational perspective, with specific classification of geometries.

Findings

Reproduces the Standard Model gauge group and particles

Predicts the number of generations as an input

Couples the Standard Model to gravity via spectral action

Abstract

The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation: space-time has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F. The raison d'etre for F is to correct the K-theoretic dimension from four to ten (modulo eight). We classify the irreducible finite noncommutative geometries of K-theoretic dimension six and show that the dimension (per generation) is a square of an integer k. Under an additional hypothesis of quaternion linearity, the geometry which reproduces the Standard Model is singled out (and one gets k=4)with the correct quantum numbers for all fields. The spectral action applied to the product MxF delivers the full Standard Model,with neutrino mixing, coupled to gravity, and makes predictions(the number of generations is still an input).