The Scalar Potential in Noncommutative Geometry

TL;DR

This paper derives the form of the scalar potential in noncommutative geometry-based Yang-Mills theory, highlighting the role of constraints on mass matrices and their relation to a prepotential function.

Contribution

It provides a general derivation of the scalar potential in noncommutative geometry Yang-Mills theories, emphasizing the conditions for non-trivial potentials without flat directions.

Findings

Non-trivial scalar potential obtained with constraints on mass matrices.

Potential related to a prepotential function.

Elimination of auxiliary fields influences the potential form.

Abstract

We present a derivation of the general form of the scalar potential in Yang-Mills theory of a non-commutative space which is a product of a four-dimensional manifold times a discrete set of points. We show that a non-trivial potential without flat directions is obtained after eliminating the auxiliary fields only if constraints are imposed on the mass matrices utilised in the Dirac operator. The constraints and potential are related to a prepotential function.