Vector/tensor duality in the five dimensional supersymmetric Green-Schwarz mechanism

TL;DR

This paper explores the supersymmetric duality between vector and tensor descriptions of the five-dimensional Green-Schwarz mechanism, revealing modifications to duality relations and boundary mass term differences.

Contribution

It introduces supersymmetric extensions of dual theories in five dimensions and derives new duality relations, including a novel chiral Chern-Simons multiplet.

Findings

Duality relations between vector and tensor formulations are established.

Boundary mass terms differ between formulations but yield identical physical spectra.

The lowest Kaluza-Klein mode acquires a finite mass in both descriptions.

Abstract

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.