The Tensor Hierarchies of Pure N=2,d=4,5,6 Supergravities

TL;DR

This paper analyzes the tensor hierarchies in pure N=2 supergravities across dimensions 4, 5, and 6, comparing gauged and ungauged cases, and explores their implications for p-brane worldvolume actions.

Contribution

It provides a comprehensive comparison of tensor hierarchies in gauged and ungauged N=2 supergravities and examines the effects of gauging on top-form symmetries and p-brane constructions.

Findings

Complete agreement in ungauged theories.

Gauging introduces Stueckelberg symmetries reducing physical top-forms.

Relations established between tensor hierarchies and p-branes.

Abstract

We study the supersymmetric tensor hierarchy of pure (gauged) N=2,d=4,5,6 supergravity and compare them with those of the pure, ungauged, theories (worked out by Gomis and Roest for d=5) and the predictions of the Kac-Moody approach made by Kleinschmidt and Roest. We find complete agreement in the ungauged case but we also find that, after gauging, new Stueckelberg symmetries reduce the number of independent "physical" top-forms. The analysis has to be performed to all orders in fermion fields. We discuss the construction of the worldvolume effective actions for the p-branes which are charged with respect to the (p+1)-form potentials and the relations between the tensor hierarchies and p-branes upon dimensional reduction.