An SL ( 2 , R ) - covariant , first order , κ - supersymmetric action for the D 5 - brane †

The new first order, rheonomic, κ–supersymmetric formalism recently introduced by us for the world-volume action of the D3 brane is extended to the case of D5 branes. This extension requires the dual formulation of the Free Differential Algebra of type IIB supergravity in terms of 6–form gauge potentials which was so far missing and is given here. Furthermore relying on our new approach we are able to write the D5 world volume action in a manifestly SL(2,R) covariant form. This is important in order to solve the outstanding problem of finding the appropriate boundary actions of D3–branes on smooth ALE manifolds with twisted fields. The application of our results to this problem is however postponed to a subsequent publication. † This work is supported in part by the European Union RTN contracts HPRN-CT-2000-00122 and HPRN-CT-200000131.