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

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 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.