Fermions in the Presence of the Antisymmetric Fields

In this manuscript we study the Dirac action in the presence of the Ramond-Ramond (R-R) potentials as gauge fields. Therefore, for the R-R field $A_{\mu_1...\mu_{p+1}}$, we identify the corresponding fermion with an extended $p$-dimensional object, which we call it F$p$-brane. Conservation of the tensor currents, associated to these fermionic branes, imposes an external tensor current. This external current enables us to study the R-R fields and their Hodge dual fields as independent degrees of freedom. We observe that an F$p$-brane should live with its dual brane, $i.e.$ F$(d-p-2)$-brane. The gauge symmetry and some other properties of a system of an F$p$-brane and its dual object will be discussed.