Gauge Theories, Duality Relations and the Tensor Hierarchy

Understand

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e.

• sets of p-form fields, with $1\le p\le D$, which realize an off-shell algebra of bosonic gauge transformations.
• We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor.
• These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion.