Supersymmetric QCD and noncommutative geometry

Abstract

We derive supersymmetric quantum chromodynamics from a noncommutative manifold, using the spectral action principle of Chamseddine and Connes. After a review of the Einstein-Yang-Mills system in noncommutative geometry, we establish in full detail that it possesses supersymmetry. This noncommutative model is then extended to give a theory of quarks, squarks, gluons and gluinos by constructing a suitable noncommutative spin manifold (i.e. a spectral triple). The particles are found at their natural place in a spectral triple: the quarks and gluinos as fermions in the Hilbert space, the gluons and squarks as bosons as the inner fluctuations of a (generalized) Dirac operator by the algebra of matrix-valued functions on a manifold. The spectral action principle applied to this spectral triple gives the Lagrangian of supersymmetric QCD, including soft supersymmetry breaking mass terms for the squarks. We find that these results are in good agreement with the physics literature.

References in corpus (17)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Gravity and the standard model with neutrino mixing
• The Soft Supersymmetry-Breaking Lagrangian: Theory and Applications
• A Universal Action Formula
• Why the Standard Model
• On Euclidean spinors and Wick rotations
• Generalized Fierz identities
• Classification of Finite Spectral Triples
• Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• On the spectral characterization of manifolds
• Connection between Space-Time Supersymmetry and Non-Commutative Geometry
• Spectral action and neutrino mass
• A continuous Wick rotation for spinor fields and supersymmetry in Euclidean space
• Supersymmetry and Noncommutative Geometry
• Remarks on the Spectral Action Principle

Cited by in corpus (15)

• Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
• Life at the Interface of Particle Physics and String Theory
• Particle Physics from Almost Commutative Spacetimes
• Noncommutative spectral geometry, algebra doubling and the seeds of quantization
• A survey of spectral models of gravity coupled to matter
• The coupling of topology and inflation in Noncommutative Cosmology
• Coupling of gravity to matter, spectral action and cosmic topology
• Space-Time from the spectral point of view
• Going beyond the Standard Model with noncommutative geometry
• Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
• Noncommutative Spectral Geometry: A Short Review
• Supersymmetry and noncommutative geometry Part I: Supersymmetric almost-commutative geometries
• Supersymmetric QCD in the Noncommutative Geometry
• Toward Supergravity Spectral Action
• Supersymmetry and the Spectral Action. On a geometrical interpretation of the MSSM