Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems

TL;DR

This work develops a unified, group-theoretical framework for gauged maximal supergravities via the embedding-tensor formalism, showing how the gauge group embeds into the duality group ${\rm G}$ and how consistency requires linear and quadratic constraints on the embedding tensor. Building on the five-dimensional vector-tensor construction, the authors introduce a hierarchy of vector and tensor fields that transform covariantly under ${\rm G}$ for arbitrary gaugings, including a generalized tensor $Z^{M,I}$ and associated objects $Y_{IM}{}^J$. They derive covariant field strengths ${\cal H}_{\mu\nu}{}^M$ and higher-rank field strengths ${\cal H}_{\mu\nu\rho I}$, introducing higher gauge transformations and a rank-3 tensor $S_{\mu\nu\rho I}{}^M$, thereby extending the d=5 results to other dimensions. Across $d=4$–$d=7$, the paper identifies the correct ${\rm G}$-representations for embedding tensors and tensor fields, predicts topological couplings such as ${\cal H}\wedge B$, ${\cal H}\wedge S$, and $S\wedge D S$, and demonstrates how these structures ensure covariance and consistency of the gauged theories in a dimension-spanning framework.

Abstract

We describe generalizations of the manifestly E_{6(6)} covariant formulation of five-dimensional gauged maximal supergravity with regard to the structure of the vector and tensor fields. We indicate how the group-theoretical structures that we discover seem to play a role in gauged supergravities in various space-time dimensions.