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

Abstract

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

6 pages