Gauge symmetry breaking in ten-dimensional Yang-Mills theory dynamically compactified on S^6

TL;DR

This paper investigates gauge symmetry breaking in ten-dimensional Yang-Mills theory with higher derivative terms, focusing on a dynamically compactified spacetime with a six-sphere, revealing a Higgs-like mechanism for gauge fields.

Contribution

It demonstrates how zero modes from the compactification are absorbed into gauge fields, resulting in massive vectors with masses influenced by higher derivative terms.

Findings

Zero modes are absorbed into gauge fields, forming massive vectors.

Mass of vector fields scales inversely with sphere radius.

Higher derivative terms increase vector masses beyond standard expectations.

Abstract

We study fluctuation modes in ten-dimensional Yang-Mills theory with a higher derivative term for the gauge field. We consider the ten-dimensional space-time to be a product of a four-dimensional space-time and six-dimensional sphere which exhibits dynamical compactification. Because of the isometry on S^6, there are flat directions corresponding to the Nambu-Goldstone zero modes in the effective theory on the solution. The zero modes are absorbed into gauge fields and form massive vector fields as a consequence of the Higgs-Kibble mechanism. The mass of the vector fields is proportional to the inverse of the radius of the sphere and larger than the mass scale set by the radius because of the higher derivative term.