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Duality orbits of non-geometric fluxes

G. Dibitetto, J. J. Fernandez-Melgarejo, D. Marques, D. Roest

TL;DR

This work demonstrates a clear dichotomy: all duality orbits in maximal $D\ge 7$ supergravities have geometric higher-dimensional origins, whereas half-maximal theories exhibit non-geometric T-duality orbits that necessitate genuinely doubled backgrounds in double field theory. By systematizing the embedding-tensor deformations and their quadratic constraints across $D=9$ and $D=8$ (maximal) and $D=8$ and $D=7$ (half-maximal), the authors show that DFT provides the higher-dimensional uplift for non-geometric cases through Scherk–Schwarz twists, including specifically constructed twisted doubles and $SO(n,n)$ embeddings. They also reveal degeneracies where the same gauging arises from distinct twist orbits, and highlight that relaxing the weak/strong constraints is essential to capture truly doubled backgrounds. The results have implications for understanding the stringy origin of non-geometric fluxes, the role of duality covariant formalisms, and the potential extension to broader theories beyond NSNS sectors. Overall, the paper clarifies when duality covariant frameworks add genuine new physics versus when they simply recast known higher-dimensional reductions.

Abstract

Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory.

Duality orbits of non-geometric fluxes

TL;DR

This work demonstrates a clear dichotomy: all duality orbits in maximal supergravities have geometric higher-dimensional origins, whereas half-maximal theories exhibit non-geometric T-duality orbits that necessitate genuinely doubled backgrounds in double field theory. By systematizing the embedding-tensor deformations and their quadratic constraints across and (maximal) and and (half-maximal), the authors show that DFT provides the higher-dimensional uplift for non-geometric cases through Scherk–Schwarz twists, including specifically constructed twisted doubles and embeddings. They also reveal degeneracies where the same gauging arises from distinct twist orbits, and highlight that relaxing the weak/strong constraints is essential to capture truly doubled backgrounds. The results have implications for understanding the stringy origin of non-geometric fluxes, the role of duality covariant formalisms, and the potential extension to broader theories beyond NSNS sectors. Overall, the paper clarifies when duality covariant frameworks add genuine new physics versus when they simply recast known higher-dimensional reductions.

Abstract

Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory.

Paper Structure

This paper contains 13 sections, 77 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Orbits from double field theory
  3. DFT and (half-)maximal gauged supergravities
  4. Parametrisations of the duality twists
  5. U-duality orbits of maximal supergravities
  6. Orbits and origin of the $D=9$ maximal case
  7. Orbits and origin of the $D=8$ maximal case
  8. T-duality orbits of half-maximal supergravities
  9. Orbits and origin of the $D=8$ half-maximal case
  10. Orbits and origin of the $D=7$ half-maximal case
  11. Conclusions
  12. Different solvable and nilpotent gaugings
  13. SO($2,2$) and SO($3,3$) 't Hooft symbols

Figures (1)

  • Figure 1: The space of flux configurations sliced into duality orbits (vertical lines). Moving along a given orbit corresponds to applying dualities to a certain flux configuration and hence it does not imply any physical changes in the lower-dimensional effective description. Geometric fluxes only constitute a subset of the full configuration space. Given an orbit, the physically relevant question is whether (orbit 2 between A and B) or not (orbit 1) this intersects the geometric subspace. We refer to a given point in an orbit as a representative.