A nonperturbative form of the spectral action principle 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.

arXiv comment12 pages. LaTeX2e, instructions for obsolete LaTeX's

References in corpus (8)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• A Universal Action Formula
• Gravity, Non-Commutative Geometry and the Wodzicki Residue
• Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
• General Relativity in terms of Dirac Eigenvalues
• Can Conformal Weyl Gravity be Considered a Viable Cosmological Theory?
• QED in external fields from the spin representation

Cited by in corpus (8)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• A survey of spectral models of gravity coupled to matter
• Quantum gauge models without classical Higgs mechanism
• Superconnections, Anomalies and Non-BPS Brane Charges
• A reconstruction theorem for almost-commutative spectral triples
• Path Integral Quantisation of Finite Noncommutative Geometries
• Gauge Theories of Dirac Type
• Internal Space for the Noncommutative Geometry Standard Model and Strings