Internal Space for the Noncommutative Geometry Standard Model and Strings

TL;DR

This paper explores the relationship between noncommutative geometry approaches to the standard model and internal spaces derived from string theory, proposing a connection via spectral actions and compactifications.

Contribution

It suggests that internal noncommutative manifolds from string theory could produce the almost commutative geometries used in the spectral action approach to the standard model.

Findings

Internal noncommutative manifolds may arise from string compactifications.

Spectral action can be linked to string-derived internal spaces.

Speculative connection between string vertex operators and noncommutative geometry.

Abstract

In this paper I discuss connections between the noncommutative geometry approach to the standard model on one side, and the internal space coming from strings on the other. The standard model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.