Abstract
We prove that for arbitrary black brane solutions of generic Supergravities there is an adapted system of variables in which the equations of motion are exactly invariant under electric–magnetic duality, i.e. the interchange of a given extended object by its electromagnetic dual. We obtain thus a procedure to automatically construct the electromagnetic dual of a given brane without needing to solve any further equation. We apply this procedure to construct the non-extremal (p,q)-string of Type-IIB String Theory (new in the literature), explicitly showing how the dual (p,q)-five-brane automatically arises in this construction. In addition, we prove that the system of variables used is suitable for a generic characterization of every double-extremal Supergravity brane solution, which we perform in full generality.
Highlights
We prove that for arbitrary black brane solutions of generic Supergravities there is an adapted system of variables in which the equations of motion are exactly invariant under electric-magnetic duality, i.e. the interchange of a given extended object by its electromagnetic dual
We prove that the system of variables used is suitable for a generic characterization of every double-extremal Supergravity brane solution, which we perform in full generality
Supergravity branes have played a role of outermost importance in String Theory since they were discovered to be the macroscopic counterparts of many String Theory microscopic extended objects, during the second String Revolution [1]
Summary
Where qΛ′ = AΩΛqΩ, A ∈Gl(nA, R), the FGK-system is invariant under the transformation (11), up to a redefinition of the charges, and with the same solution of the FGK-system we can construct two space-time solutions, the electric-brane solution and the magneticbrane solution. In order to see when condition (12) holds, we have to change from electric variables AΛ(p+1) to the magnetic ones A(p+1)Λ in the action (1). The equations of motion and the Bianchi identities for the electric fields AΛ(p+1) are d IΛΩ ∗ F(Ωp+2) = 0 , dF(Λp+2) = 0 .
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