Space-Time from the spectral point of view

TL;DR

This paper presents a spectral geometric approach to modeling space-time, integrating finite geometries to encode its fine structure, and demonstrates how this framework can derive the Standard Model coupled with gravity.

Contribution

It introduces a spectral geometric paradigm for space-time that incorporates finite geometries, leading to a derivation of the Standard Model from pure gravity.

Findings

Finite geometries classify space-time structure.

The symplectic--unitary geometry yields Standard Model plus gravity.

Testable predictions emerge at unification scale.

Abstract

We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new paradigm to model space-time whose fine structure can be encoded by a finite geometry. The classification of the irreducible finite geometries of KO-dimension 6 singles out a ``symplectic--unitary" candidate F, which when used as the fine texture of space-time delivers from pure gravity on M x F the Standard Model coupled to gravity and, once extrapolated to unification scale, gives testable predictions.