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U-dual fluxes and Generalized Geometry

G. Aldazabal, E. Andres, P. G. Camara, M. Graña

TL;DR

This work develops Exceptional Generalized Geometry ($EGG$) as a unifying framework for string flux compactifications, establishing a precise dictionary between fluxes, 4d gauged supergravity gaugings, and $E_7$ representations. It identifies all gaugings that admit uplifts to 10d heterotic or type IIB backgrounds, uncovering new RR deformations that extend the familiar $β$-deformation to RR sectors and to F-theory backgrounds via $γ$-deformations. The authors provide explicit, covariant expressions for the 4d superpotential in arbitrary $\mathcal{N}=1$ heterotic or type IIB orientifold compactifications, incorporating the full dual flux content and their geometric vs non-geometric nature. The results bridge 10d origins and 4d effective theories, offering a robust toolkit for exploring moduli stabilization, dualities, and the landscape of flux vacua in both toroidal and more general $SU(3)$-structure compactifications.

Abstract

We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the $β$-deformation. These new deformations are expected to provide the natural extension of the $β$-deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary N = 1 heterotic or type IIB orientifold compactifications, for all the allowed fluxes.

U-dual fluxes and Generalized Geometry

TL;DR

This work develops Exceptional Generalized Geometry () as a unifying framework for string flux compactifications, establishing a precise dictionary between fluxes, 4d gauged supergravity gaugings, and representations. It identifies all gaugings that admit uplifts to 10d heterotic or type IIB backgrounds, uncovering new RR deformations that extend the familiar -deformation to RR sectors and to F-theory backgrounds via -deformations. The authors provide explicit, covariant expressions for the 4d superpotential in arbitrary heterotic or type IIB orientifold compactifications, incorporating the full dual flux content and their geometric vs non-geometric nature. The results bridge 10d origins and 4d effective theories, offering a robust toolkit for exploring moduli stabilization, dualities, and the landscape of flux vacua in both toroidal and more general -structure compactifications.

Abstract

We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the -deformation. These new deformations are expected to provide the natural extension of the -deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary N = 1 heterotic or type IIB orientifold compactifications, for all the allowed fluxes.

Paper Structure

This paper contains 23 sections, 122 equations, 6 tables.

Table of Contents

  1. Introduction
  2. Generalized Geometry
  3. $O(d,d)$ structure
  4. T-dual field strengths
  5. Exceptional Generalized Geometry and U-dual gauge fields
  6. The $\hbox{\bf 56}$ representation of the gauge parameters
  7. The $\hbox{\bf 133}$ representation of the gauge fields
  8. From $E_7$ to $O(6,6) \times \mathop{\mathrm{\mathit{SL}}}\nolimits(2,\mathbb{R})$
  9. U-dual field strengths
  10. Toroidal compactifications and dual fluxes
  11. U-dual gauge algebra and constraints
  12. Toroidal orbifolds and flux induced superpotentials
  13. Type IIB orientifold compactifications
  14. Heterotic orbifold compactifications
  15. General $\mathcal{N}=1$ compactifications
  16. ...and 8 more sections