Fermions in the Presence of the Antisymmetric Fields

TL;DR

This paper explores the interaction of fermionic p-branes with Ramond-Ramond fields, revealing duality relations and gauge symmetries in string theory contexts.

Contribution

It introduces the concept of fermionic p-branes (F$p$-branes) and analyzes their gauge properties and duality with other branes in the presence of antisymmetric R-R fields.

Findings

F$p$-branes are associated with extended fermionic objects in R-R backgrounds.

F$p$-branes must coexist with their dual F$(d-p-2)$-branes.

The gauge symmetry of the combined system is characterized and discussed.

Abstract

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.