The five dimensional version of the Green-Schwarz mechanism can be invoked to cancel U(1) anomalies on the boundaries of brane world models. In five dimensions there are two dual descriptions that employ either a two-form tensor field or a vector field. We present the supersymmetric extensions of these dual theories using four dimensional $N=1$ superspace. For the supersymmetrization of the five dimensional Chern-Simons three-form this requires the introduction of a new chiral Chern-Simons multiplet. We derive the supersymmetric vector/tensor duality relations and show that not only is the usual one-/two-form duality modified, but that there is also an interesting duality relation between the scalar components. Furthermore, the vector formulation always contains singular boundary mass terms which are absent in the tensor formulation. This apparent inconsistency is resolved by showing that in either formulation the four dimensional anomalous U(1) mass spectrum is identical, with the lowest lying Kaluza-Klein mode generically obtaining a finite nonzero mass.

• Received 21 April 2004

DOI:https://doi.org/10.1103/PhysRevD.70.086012