Trombone gaugings of five-dimensional maximal supergravity

TL;DR

The paper advances the classification of five-dimensional maximal supergravities by incorporating trombone gaugings, describing the full set of field equations and supersymmetry variations with the embedding-tensor formalism. It introduces the new family ${\rm TCSO}(p,q,r;\rho)$ of gaugings inside ${\mathbb R}^+ \times SL(2,\mathbb{R}) \times SL(6,\mathbb{R})$, and analyzes a concrete example ${\rm TCSO}(5,0,1;1)$, showing equivalence to known frames and identifying a consistent ${\cal N}=2$ subsector that yields supersymmetric AdS vacua. The AdS solutions MN2, MN1 and BBBW are obtained within this framework, with explicit mass spectra organized into supermultiplets and uplifting to eleven-dimensional AdS$_5$ solutions. The work thereby extends the landscape of gauged supergravities to include trombone contributions and links five-dimensional vacua to M5-brane CFT phases, providing a foundation for further holographic and higher-dimensional studies.

Abstract

The maximal gauged supergravities in five spacetime dimensions with gauge groups contained in $\mathbb{R}^+ \times \textrm{E}_{6(6)}$ are described. The $\textrm{E}_{6(6)}$ factor is the duality group of ungauged maximal supergravity and $\mathbb{R}^+$ is the scaling symmetry of the five-dimensional metric, usually called the \textit{trombone} symmetry. The equations of motion and supersymmetry variations for these supergravities are given to lowest order in fermions, and the mass matrices are provided. Then, the theories with gauge groups contained in a maximal subgroup of $\mathbb{R}^+ \times \textrm{E}_{6(6)}$ are classified, and a new family of such supergravities uncovered. For a concrete theory in this class, some supersymmetric anti-de Sitter vacua are found and their mass spectra computed within the gauged supergravity. These vacua are argued to be related to superconformal phases of the M5-brane field theory.