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How to uplift non-maximal gauged supergravities

Davide Rovere, Colin Sterckx

TL;DR

This work develops a systematic framework to uplift non-maximal gauged supergravities to ten-/eleven-dimensional supergravity using Exceptional Field Theory and generalized geometry. By requiring the internal manifold to admit a ${ rak g}_g$-action and reducing the consistency condition to a PDE on the base $M_{ ext{int}}/G_g$, the authors classify uplifts via generalized $G_S$-structures with constant intrinsic torsion identified with the embedding tensor. They provide a concrete M-theory embedding for an ${ m N}=4$ D=4 nv=6 theory and, more broadly, classify Type IIB uplifts of pure ${ m N}=4$ D=4 gauged supergravity, obtaining consistent truncations around the DHoker–Estes–Gutperle AdS$_4$ solutions through an explicit ExFT-to-SUGRA dictionary. This approach extends gSS methods beyond maximal/pure truncations, offering a principled path to new uplifts and holographic applications, including brane probes and black hole studies in non-maximal contexts. The work also outlines future directions, such as uplifts to massive IIA, lower dimensions via ${ m E}_{8(8)}$ ExFT, and exploring other ${ m N}=2/3$ gaugings with the same methodology.

Abstract

In this paper, we provide an algorithm to perform the uplift of non-maximal $G_g$-gauged supergravities to type IIB or 11D supergravities. Using tools of exceptional field theory and generalised geometry, we show that the internal manifold admits a $G_g$-action, and that consistency of the uplift is equivalent to solving a simpler PDE on the quotient $M_{\text{int}}/G_g$. As an application, we classify all possible uplifts of pure half-maximal four-dimensional $\textrm{SO}(4)$-gauged supergravity to type IIB and we recover consistent truncations around any of the D'Hoker-Estes-Gutperle solutions \cite{DHoker:2007hhe}.

How to uplift non-maximal gauged supergravities

TL;DR

This work develops a systematic framework to uplift non-maximal gauged supergravities to ten-/eleven-dimensional supergravity using Exceptional Field Theory and generalized geometry. By requiring the internal manifold to admit a -action and reducing the consistency condition to a PDE on the base , the authors classify uplifts via generalized -structures with constant intrinsic torsion identified with the embedding tensor. They provide a concrete M-theory embedding for an D=4 nv=6 theory and, more broadly, classify Type IIB uplifts of pure D=4 gauged supergravity, obtaining consistent truncations around the DHoker–Estes–Gutperle AdS solutions through an explicit ExFT-to-SUGRA dictionary. This approach extends gSS methods beyond maximal/pure truncations, offering a principled path to new uplifts and holographic applications, including brane probes and black hole studies in non-maximal contexts. The work also outlines future directions, such as uplifts to massive IIA, lower dimensions via ExFT, and exploring other gaugings with the same methodology.

Abstract

In this paper, we provide an algorithm to perform the uplift of non-maximal -gauged supergravities to type IIB or 11D supergravities. Using tools of exceptional field theory and generalised geometry, we show that the internal manifold admits a -action, and that consistency of the uplift is equivalent to solving a simpler PDE on the quotient . As an application, we classify all possible uplifts of pure half-maximal four-dimensional -gauged supergravity to type IIB and we recover consistent truncations around any of the D'Hoker-Estes-Gutperle solutions \cite{DHoker:2007hhe}.

Paper Structure

This paper contains 62 sections, 6 theorems, 174 equations.

Table of Contents

  1. Introduction
  2. How to uplift a gauged supergravity?
  3. Plan of the paper
  4. Review of ExFT and consistent truncations
  5. Generalised geometry and exceptional field theory
  6. The ${\mathrm{E}_{7(7)}}$ generalised Lie derivative in type IIB
  7. The ${\mathrm{E}_{7(7)}}$ generalised Lie derivative in M-theory
  8. Systematics of consistent truncations
  9. Reduction of the structure group
  10. Intrinsic torsion
  11. Truncation ansatz
  12. Construction of an uplift
  13. The internal manifold
  14. A local model for ${M_{\text{int}}}$
  15. Homogeneous spaces
  16. ...and 47 more sections

Key Result

Theorem 1

Let $\xi \rightarrow \xi_M$ be a Lie algebra action on a manifold $M$, this action integrate to the action of the associated simply connected Lie group $G$ if and only if each $\xi_M$ is complete.

Theorems & Definitions (14)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Definition 3
  • Example
  • Definition 4
  • Definition 5
  • Theorem 2: Slice theorem for proper action
  • Example
  • Theorem 3: Orbit type stratification
  • ...and 4 more