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T-dualities and scale-separated AdS$_3$ in massless IIA on $(X_6 \times S^1)/\mathbb{Z}_2$

George Tringas

Abstract

Motivated by the question of whether scale-separated AdS$_3$ flux vacua arising from G$_2$ compactifications admit an uplift to eleven-dimensional supergravity, we construct scale-separated AdS$_3$ flux vacua in massless type IIA with only O6-planes. We first present new scale-separated solutions in massive type IIA on a G$_2$ holonomy toroidal orbifold with four smeared O6-planes, analyze their properties, and then perform a double T-duality to obtain the corresponding massless backgrounds. In the dual frame, the internal space is locally given by a six-dimensional quotient space $X_6$ with an $\mathrm{SU}(3)$ structure of Iwasawa type times an untwisted circle $S^1$, while globally it is further modded out by a non-trivial $\mathbb{Z}_2$ quotient inherited from the G$_2$ orbifold action. Finally, we use T-duality to derive the corresponding superpotential in massless type IIA and identify parametrically classical, scale-separated families of solutions, as well as a family with parametrically large radii, scale separation, and strong coupling, thus allowing for an uplift to eleven-dimensional supergravity.

T-dualities and scale-separated AdS$_3$ in massless IIA on $(X_6 \times S^1)/\mathbb{Z}_2$

Abstract

Motivated by the question of whether scale-separated AdS flux vacua arising from G compactifications admit an uplift to eleven-dimensional supergravity, we construct scale-separated AdS flux vacua in massless type IIA with only O6-planes. We first present new scale-separated solutions in massive type IIA on a G holonomy toroidal orbifold with four smeared O6-planes, analyze their properties, and then perform a double T-duality to obtain the corresponding massless backgrounds. In the dual frame, the internal space is locally given by a six-dimensional quotient space with an structure of Iwasawa type times an untwisted circle , while globally it is further modded out by a non-trivial quotient inherited from the G orbifold action. Finally, we use T-duality to derive the corresponding superpotential in massless type IIA and identify parametrically classical, scale-separated families of solutions, as well as a family with parametrically large radii, scale separation, and strong coupling, thus allowing for an uplift to eleven-dimensional supergravity.

Paper Structure

This paper contains 30 sections, 181 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Orbifold for new massive and massless IIA
  3. Fluxes and tadpole cancellation
  4. Kaluza--Klein states
  5. Moduli stabilization and families of solutions
  6. Families of solutions.
  7. Double T-duality
  8. Tadpole cancellation
  9. Geometry of the massless IIA background
  10. G2 splitting and SU(3) structure on X6
  11. Fluxes in 6+1 language and orientifold projections
  12. Orientifold projections.
  13. Scalar degrees of freedom
  14. Differential relations and torsion classes
  15. G$_2$ perspective.
  16. ...and 15 more sections

Figures (1)

  • Figure 1: Left: The orientifold involutions in the massive type IIA setup. Right: The orientifold involutions generated by the double T-duality in \ref{['systemT']}. Wrapped directions are marked by $\times$, while localized positions are indicated by $-$. We emphasize once again that the O2- and O4-planes are canceled by D-branes.