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All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua

Davide Cassani, Paul Koerber, Oscar Varela

TL;DR

This work constructs a comprehensive dimensional reduction of 11D supergravity on seven-dimensional manifolds with SU(3)-structure, yielding 4D N=2 gauged supergravity with rich electric and magnetic gaugings. Using a finite left-invariant basis of forms and geometric fluxes, the authors derive a consistent truncation that naturally produces non-abelian vector gaugings and Heisenberg-type hyperscalar gaugings, with the 4D action matching the standard N=2 gauged supergravity framework. Specializing to all homogeneous SU(3)-structure cosets that support supersymmetric AdS$_4$ vacua (including S^7, M$^{110}$, Q$^{111}$, V$_{5,2}$, and Aloff-Wallach spaces N(k,l)), they obtain explicit scalar manifolds, gaugings, and vacuum structures, revealing a spectrum of vacua with N=2 and N=1 supersymmetry as well as a new non-supersymmetric AdS point in some models. The results unify Sasaki-Einstein and weak G$_2$-type structures within a single LI truncation framework and extend known reductions to new gaugings, enriching the M-theory landscape for holography and moduli stabilization.

Abstract

We study consistent truncations of M-theory to gauged N=2 supergravity in four dimensions, based on a large class of SU(3)-structures in seven dimensions. We show that the gauging involves isometries of the vector multiplet scalar manifold as well as the Heisenberg algebra and a special isometry of the hyperscalar manifold. As a result, non-abelian gauge groups and new non-trivial scalar potentials are generated. Then we specialize to all homogeneous SU(3)-structures supporting supersymmetric AdS4 vacua. These are the Stiefel manifold V52, the Aloff-Wallach spaces N(k,l), the seven-sphere (seen as SU(4)/SU(3) or Sp(2)/Sp(1)) and the M110 and Q111 coset spaces. For each of these cases, we describe in detail the N=2 model and discuss its peculiarities.

All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua

TL;DR

This work constructs a comprehensive dimensional reduction of 11D supergravity on seven-dimensional manifolds with SU(3)-structure, yielding 4D N=2 gauged supergravity with rich electric and magnetic gaugings. Using a finite left-invariant basis of forms and geometric fluxes, the authors derive a consistent truncation that naturally produces non-abelian vector gaugings and Heisenberg-type hyperscalar gaugings, with the 4D action matching the standard N=2 gauged supergravity framework. Specializing to all homogeneous SU(3)-structure cosets that support supersymmetric AdS vacua (including S^7, M, Q, V, and Aloff-Wallach spaces N(k,l)), they obtain explicit scalar manifolds, gaugings, and vacuum structures, revealing a spectrum of vacua with N=2 and N=1 supersymmetry as well as a new non-supersymmetric AdS point in some models. The results unify Sasaki-Einstein and weak G-type structures within a single LI truncation framework and extend known reductions to new gaugings, enriching the M-theory landscape for holography and moduli stabilization.

Abstract

We study consistent truncations of M-theory to gauged N=2 supergravity in four dimensions, based on a large class of SU(3)-structures in seven dimensions. We show that the gauging involves isometries of the vector multiplet scalar manifold as well as the Heisenberg algebra and a special isometry of the hyperscalar manifold. As a result, non-abelian gauge groups and new non-trivial scalar potentials are generated. Then we specialize to all homogeneous SU(3)-structures supporting supersymmetric AdS4 vacua. These are the Stiefel manifold V52, the Aloff-Wallach spaces N(k,l), the seven-sphere (seen as SU(4)/SU(3) or Sp(2)/Sp(1)) and the M110 and Q111 coset spaces. For each of these cases, we describe in detail the N=2 model and discuss its peculiarities.

Paper Structure

This paper contains 34 sections, 235 equations, 1 figure, 10 tables.

Table of Contents

  1. Introduction
  2. SU(3)-structures and their moduli space
  3. SU(3)-structures in seven dimensions
  4. A finite-dimensional space of SU(3)-structures
  5. Special Kähler geometry on the space of deformations
  6. The dimensional reduction
  7. The truncation ansatz
  8. The 4D action
  9. The $N=2$ gauging
  10. The action with magnetic vectors
  11. The gauging
  12. Explicit models from coset reduction
  13. The scalar manifolds
  14. The gaugings
  15. Salient features
  16. ...and 19 more sections

Figures (1)

  • Figure 1: Web of interrelated consistent truncations of 11D (blue), type IIA (red) and type IIB (purple) supergravity. The diagram is based on figure 1 in caskoerbertrisak, but updated with the coset models discussed in this paper. In each box we display the geometric structure (if any) and the coset manifold on which the truncation is based, as well as its amount of supersymmetry. Each arrow denotes a consistent subtruncation. Note that the Nearly-Kähler truncation cannot be reached directly from the $N(1,1)$ and Sp(2)/Sp(1) models, since the respective choices of $m^i$ geometric fluxes are incompatible.