Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions

TL;DR

This work constructs and classifies maximally supersymmetric gauged supergravities in three dimensions by reformulating the consistency of gaugings as a single $E_{8(8)}$-covariant projector condition ${f P}_{27000}\Theta=0$ on the embedding tensor. The theory introduces a field-dependent $T$-tensor built from the scalar vielbein ${rak V}$ and the embedding tensor, with linear, differential, and quadratic identities ensuring maximal supersymmetry; the $A_{1,2,3}$ Yukawa tensors are determined in terms of $T$, and all admissible gauge groups are identified, including a regular family $SO(p,8-p) imes SO(p,8-p)$ and several exceptional noncompact groups. Each admissible gauging yields a maximally supersymmetric AdS$_3$ ground state with background isometries that extend ${SO(2,2)}$ to an AdS supergroup pair $G_L\times G_R$, with explicit spectra and symmetry breaking patterns. The results suggest a potential higher-dimensional origin beyond conventional $D=11$ supergravity, possibly involving a generalized 248-vector framework and a CS-like higher-dimensional formulation, highlighting new avenues for holography in AdS$_3$/CFT$_2$ contexts.

Abstract

We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions -- especially the on-shell duality between vector and scalar fields, and the purely topological character of (super)gravity -- they exhibit an even richer structure than the gauged supergravities in higher dimensions. The allowed gauge groups are subgroups of the global E_8 symmetry of ungauged N=16 supergravity. They include the regular series SO(p,8-p) x SO(p,8-p) for all p=0,1,...,4, the group E_8 itself, as well as various noncompact forms of the exceptional groups E_7, E_6 and F_4 x G_2. We show that all these theories admit maximally supersymmetric ground states, and determine their background isometries, which are superextensions of the anti-de Sitter group SO(2,2). The very existence of these theories is argued to point to a new supergravity beyond the standard D=11 supergravity.