New Type of Vector Gauge Theory from Noncommutative Geometry

TL;DR

This paper introduces a novel vector gauge theory derived from noncommutative geometry that features a shift-like symmetry, enabling mass generation for vector fields without the Higgs mechanism.

Contribution

It presents a new class of gauge theories using superconnection formalism with a matrix derivative, leading to mass terms without Higgs fields.

Findings

Constructed a vector gauge theory with shift-like symmetry.

Demonstrated mass generation for vector fields without Higgs.

Developed fermionic action within the noncommutative geometric framework.

Abstract

Using the formalism of noncommutative geometric gauge theory based on the superconnection concept, we construct a new type of vector gauge theory possessing a shift-like symmetry and the usual gauge symmetry. The new shift-like symmetry is due to the matrix derivative of the noncommutative geometric gauge theory, and this gives rise to a mass term for the vector field without introducing the Higgs field. This construction becomes possible by using a constant one form even matrix for the matrix derivative, for which only constant zero form odd matrices have been used so far. The fermionic action in this formalism is also constructed and discussed.