Space-filling branes & gaugings

TL;DR

This paper classifies supersymmetric space-filling branes in various supergravity truncations across dimensions, revealing the presence of exotic branes and their relation to gaugings and tadpole conditions.

Contribution

It provides a comprehensive analysis of BPS space-filling branes and their representations in truncated supergravity theories, including the role of exotic branes and the impact on gaugings.

Findings

Exotic branes appear in dimensions below eight.

Highest-dimensional representations relate to tadpole conditions.

Truncations affect quadratic constraints and brane configurations.

Abstract

We consider in any dimension the supersymmetric $\mathbb{Z}_2$ truncations of the maximal supergravity theories. In each dimension and for each truncation we determine all the sets of 1/2-BPS space-filling branes that preserve the supersymmetry of the truncated theory and the representations of the symmetry of such theory to which they belong. We show that in any dimension below eight these sets always contain exotic branes, that are objects that do not have a ten-dimensional origin. We repeat the same analysis for half-maximal theories and for the quarter-maximal theories in four and three dimensions. We then discuss all the possible gaugings of these theories as described in terms of the embedding tensor. In general, the truncation acts on the quadratic constraints of the embedding tensor in such a way that some representations survive the truncation although they are not required by the supersymmetry of the truncated theory. We show that for any theory, among these representations, the highest-dimensional ones are precisely those of the 1/2-BPS space-filling branes that preserve the same supersymmetry of the truncated theory, and we interpret this result as the fact that these quadratic constraints after the truncation become tadpole conditions for such branes.