Supersymmetric QCD and noncommutative geometry

TL;DR

This paper derives supersymmetric QCD within a noncommutative geometric framework using the spectral action principle, successfully incorporating particles like quarks, gluons, and their superpartners, and aligning with established physics results.

Contribution

It constructs a noncommutative geometric model of supersymmetric QCD, extending previous models to include superpartners and soft supersymmetry breaking terms.

Findings

Spectral action yields supersymmetric QCD Lagrangian.

Particles fit naturally into the spectral triple framework.

Results agree with existing physics literature.

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.