 Abelian p-form gauge field

An Abelian $p$-form gauge potential $A_p$ is an antisymmetric tensor field with gauge equivalence $A_p\mapsto A_p+d{\Lambda }_{p-1}$ and field strength $F_{p+1}=d{A}_p$. Its field strength obeys the Bianchi identity for an Abelian p-form. The potential can have global gauge data even when its local field strength vanishes.