Gauge symmetry breaking in ten-dimensional Yang-Mills theory dynamically compactified on S⁶

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.