The Gaugings of Maximal D=6 Supergravity

TL;DR

This work classifies all consistent gaugings of maximal D=6 supergravity with (2,2) supersymmetry by employing the embedding tensor in the $SO(5,5)$ duality framework. It constructs the full gauged Lagrangian, including the topological term and a deformed tensor hierarchy up to 3-forms, and expresses the scalar potential as a bilinear in the embedding tensor, $V(oldsymbol{}) = \tfrac{1}{2}\ theta^{AM} theta^{BN} \, \mathcal V_M^a \mathcal V_N^b (\bar V_A \ gamma^b gamma^a V_B)$. The gaugings decompose under ${ m GL}(5)$ into electric, magnetic, and mixed types, with explicit quadratic constraints ensuring consistency and closure; the results connect to higher-dimensional origins via Scherk–Schwarz reductions and eleven-dimensional flux compactifications, and include truncations to half-maximal theories and Romans-type deformations. Overall, the paper provides a comprehensive, covariant framework for all maximal D=6 gaugings and clarifies how duality, tensor hierarchy, and higher-form content interlock in six dimensions.

Abstract

We construct the most general gaugings of the maximal D=6 supergravity. The theory is (2,2) supersymmetric, and possesses an on-shell SO(5,5) duality symmetry which plays a key role in determining its couplings. The field content includes 16 vector fields that carry a chiral spinor representation of the duality group. We utilize the embedding tensor method which determines the appropriate combinations of these vectors that participate in gauging of a suitable subgroup of SO(5,5). The construction also introduces the magnetic duals of the 5 two-form potentials and 16 vector fields.