Spontaneous compactification of D=5 two-form gauge fields and the obtainment of Maxwell and Yang-Mills theories

TL;DR

This paper demonstrates how spontaneous compactification of 5D two-form gauge fields naturally yields 4D Maxwell and Yang-Mills theories, linking higher-dimensional gauge fields to familiar fundamental interactions.

Contribution

It provides a novel mechanism showing how 4D gauge theories emerge from 5D two-form gauge fields through spontaneous compactification.

Findings

Compactification leads to Maxwell and Yang-Mills theories from 5D two-form gauge fields.

Zero mode of the fifth component of the tensor field generates the vector potential.

Refined stress tensor definition is necessary for non-Abelian case compatibility.

Abstract

We show that the spontaneous compactification of the Abelian and non-Abelian two-form gauge field theories from $D=4+1$ to $D=3+1$ leads to the same theories plus the Maxwell and Yang-Mills ones, respectively. The vector potential comes from the zero mode of the fifth component of the tensor gauge field in D=5. Concerning to the non-Abelian case, it is necessary to make a more refined definition of the three-form stress tensor in order to be compatible, after the compactification, with the two-form stress tensor of the Yang-Mills theory.