$(p+2)$-form gauge fields for $p$-brane through an action-at-a-distance

In the conventional $p$-brane theory, a gauge ($p+1$)-form field $\phi^{(p+1)}$ mediates the interaction between $p$-branes, which is gauge invariant in the sense $\phi^{(p+1)}\to \phi^{(p+1)}+d\Lambda^{(p)}$ with $\Lambda^{(p)}$, an arbitrary $p$-form and $d$, a boundary operator. We, on the contrary, propose to introduce a new gauge field $\phi^{(p+2)}$ mediating the interaction, and we have a new type of gauge transformation: $\phi^{(p+2)}\to \phi^{(p+2)} +\delta\Lambda^{(p+3)}$, with $\delta$, a coboundary operator.