On the Magical Supergravities in Six Dimensions

TL;DR

The paper classifies all consistent gaugings of six-dimensional magical supergravities using the embedding tensor formalism, showing that the vector/tensor sector gauge group is a nilpotent, centrally extended translation group determined by a single $SO(n_T,1)$ spinor and that hypermultiplet couplings can introduce central charges acting on the hyperscalars. It also constructs the gauged theory, including the tensor hierarchy, minimal and Yukawa couplings, and a positive-definite scalar potential, and analyzes gauging of the R-symmetry and possible hypersector embeddings. The work situates these gaugings within the broader 5D uplifts and spinor-orbit classifications, and discusses anomaly constraints and string-theory implications, including anomaly-free cases such as the octonionic theory and directions for future embedding in string compactifications. Overall, the results provide a complete framework for understanding how magical 6D supergravities can be gauged while maintaining gauge invariance and supersymmetry, and highlight important open problems related to quantum anomalies and string realizations.

Abstract

Magical supergravities are a very special class of supergravity theories whose symmetries and matter content in various dimensions correspond to symmetries and underlying algebraic structures of the remarkable geometries of the Magic Square of Freudenthal, Rozenfeld and Tits. These symmetry groups include the exceptional groups and some of their special subgroups. In this paper, we study the general gaugings of these theories in six dimensions which lead to new couplings between vector and tensor fields. We show that in the absence of hypermultiplet couplings the gauge group is uniquely determined by a maximal set of commuting translations within the isometry group SO(n_T,1) of the tensor multiplet sector. Moreover, we find that in general the gauge algebra allows for central charges that may have nontrivial action on the hypermultiplet scalars. We determine the new minimal couplings, Yukawa couplings and the scalar potential.