A nonperturbative form of the spectral action principle in noncommutative geometry

TL;DR

This paper introduces a nonperturbative bosonic action functional in noncommutative geometry using superconnections, leading to Einstein gravity and Standard Model terms with a nonminimal coupling.

Contribution

It presents a nonperturbative formulation of the spectral action principle in noncommutative geometry utilizing superconnections, revealing new couplings.

Findings

Derives a bosonic action functional consistent with Einstein gravity and Standard Model terms.

Shows the emergence of an effective nonminimal coupling in the bosonic sector.

Provides a new perspective on the spectral action in noncommutative geometry.

Abstract

Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein gravity and Standard Model Yang-Mills-Higgs terms. It provides an effective nonminimal coupling in the bosonic sector of the Lagrangian.