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Gauged Supergravities in Three Dimensions: A Panoramic Overview

B. de Wit, H. Nicolai, H. Samtleben

TL;DR

This work catalogs the gauged supergravities in three dimensions up to $N=16$, highlighting an unusually large and varied landscape of possible gauge groups, including semisimple, non-semisimple, and complex gaugings. It develops a unifying framework based on the embedding tensor and the $T$-tensor to implement consistent gaugings, recasts YM gaugings as CS gaugings, and derives the full Lagrangian and supersymmetry rules subject to SUSY-consistency constraints. The authors explicitly classify admissible gauge groups for the maximal theory, showing that semisimple gaugings typically come in product forms with fixed coupling ratios, while non-semisimple and complex gaugings (e.g., ${ m SO}(8,\,C)$) yield novel vacua and dynamics, including AdS$_3$/CFT$_2$ contexts and potential links to higher-dimensional frameworks. Overall, the paper provides a comprehensive, on-shell-equivalent panorama of three-dimensional gauged supergravities, with a robust formalism applicable across different $N$ and strong implications for holography and the geometry of compactifications.

Abstract

Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we review the recent progress in constructing these theories and discuss some of their possible applications.

Gauged Supergravities in Three Dimensions: A Panoramic Overview

TL;DR

This work catalogs the gauged supergravities in three dimensions up to , highlighting an unusually large and varied landscape of possible gauge groups, including semisimple, non-semisimple, and complex gaugings. It develops a unifying framework based on the embedding tensor and the -tensor to implement consistent gaugings, recasts YM gaugings as CS gaugings, and derives the full Lagrangian and supersymmetry rules subject to SUSY-consistency constraints. The authors explicitly classify admissible gauge groups for the maximal theory, showing that semisimple gaugings typically come in product forms with fixed coupling ratios, while non-semisimple and complex gaugings (e.g., ) yield novel vacua and dynamics, including AdS/CFT contexts and potential links to higher-dimensional frameworks. Overall, the paper provides a comprehensive, on-shell-equivalent panorama of three-dimensional gauged supergravities, with a robust formalism applicable across different and strong implications for holography and the geometry of compactifications.

Abstract

Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we review the recent progress in constructing these theories and discuss some of their possible applications.

Paper Structure

This paper contains 12 sections, 88 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Supergravity coupled to nonlinear sigma models
  3. Isometries and R-symmetries
  4. Yang-Mills versus Chern-Simons gauged theories
  5. The embedding tensor
  6. $T$-tensors, consistency constraints, and the Lagrangian
  7. Discussion of low $N$ theories
  8. $N=1$
  9. $N=2$
  10. Some comments on $N=3$ and $N=4$ theories
  11. Symmetric target spaces with $N>4$
  12. Admissible gauge groups for $N=16$

Figures (1)

  • Figure 1: CS and YM gauged supergravity in three dimensions