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Exploiting N=2 in consistent coset reductions of type IIA

Davide Cassani, Amir-Kian Kashani-Poor

TL;DR

The paper demonstrates that massive Type IIA compactifications on left coset manifolds with SU(3) structure yield consistent ${N}=2$ gauged supergravity in four dimensions via a left-invariant truncation, enabling a controlled study of fluxes, adS vacua, and quantum corrections. It shows that RR fluxes and K-theory–induced quantization produce discrete families of ${N}=1$ AdS vacua, including a Nearly Kähler solution, and proves the truncation is consistent with the full 10d equations. At tree level, the ${N}=2$-gauged potential forbids de Sitter vacua, while string-loop corrections can alter this outcome under specific NSNS contributions, with a derived necessary condition for dS vacua in the loop-corrected potential. The work also uncovers non-supersymmetric AdS vacua, analyzes their stability, and discusses the persistence of these vacua to loop corrections, highlighting the robustness of the ${N}=2$ framework for exploring higher-dimensional corrections and the landscape of flux vacua.

Abstract

We study compactifications of type IIA supergravity on cosets exhibiting SU(3) structure. We establish the consistency of the truncation based on left-invariance, providing a justification for the choice of expansion forms which yields gauged N=2 supergravity in 4 dimensions. We explore N=1 solutions of these theories, emphasizing the requirements of flux quantization, as well as their non-supersymmetric companions. In particular, we obtain a no-go result for de Sitter solutions at string tree level, and, exploiting the enhanced leverage of the N=2 setup, provide a preliminary analysis of the existence of de Sitter vacua at all string loop order.

Exploiting N=2 in consistent coset reductions of type IIA

TL;DR

The paper demonstrates that massive Type IIA compactifications on left coset manifolds with SU(3) structure yield consistent gauged supergravity in four dimensions via a left-invariant truncation, enabling a controlled study of fluxes, adS vacua, and quantum corrections. It shows that RR fluxes and K-theory–induced quantization produce discrete families of AdS vacua, including a Nearly Kähler solution, and proves the truncation is consistent with the full 10d equations. At tree level, the -gauged potential forbids de Sitter vacua, while string-loop corrections can alter this outcome under specific NSNS contributions, with a derived necessary condition for dS vacua in the loop-corrected potential. The work also uncovers non-supersymmetric AdS vacua, analyzes their stability, and discusses the persistence of these vacua to loop corrections, highlighting the robustness of the framework for exploring higher-dimensional corrections and the landscape of flux vacua.

Abstract

We study compactifications of type IIA supergravity on cosets exhibiting SU(3) structure. We establish the consistency of the truncation based on left-invariance, providing a justification for the choice of expansion forms which yields gauged N=2 supergravity in 4 dimensions. We explore N=1 solutions of these theories, emphasizing the requirements of flux quantization, as well as their non-supersymmetric companions. In particular, we obtain a no-go result for de Sitter solutions at string tree level, and, exploiting the enhanced leverage of the N=2 setup, provide a preliminary analysis of the existence of de Sitter vacua at all string loop order.

Paper Structure

This paper contains 29 sections, 124 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Introducing the internal geometries
  3. The expansion forms
  4. $\frac{\textrm{SU(3)}}{\textrm{U(1)}\times \textrm{U(1)}}$
  5. $\frac{\mathrm{Sp(2)}}{\mathrm{S(U(2)}\times\mathrm{U(1))}}$
  6. $\frac{\textrm{G}_2}{\textrm{SU(3)} }$
  7. Properties
  8. The SU(3) structure
  9. An alternative basis?
  10. Supersymmetric 10d solutions parametrized by fluxes
  11. Flux quantization and $K$-theory
  12. Is it possible to have only $G_0$ and $G_6$ non-vanishing?
  13. Given $G_2=0$, which $G_4$ are permissible?
  14. The solution
  15. The dimensional reduction
  16. ...and 14 more sections

Figures (1)

  • Figure 1: The potential for $\frac{\mathrm{G}_2}{\mathrm{SU(3)}\,}$: we plot the rescaled potential $e^{\frac{5}{3}}m^{\frac{1}{3}}I^{\frac{4}{3}}V$ as a function of $(Im/e)^{\frac{1}{3}}b\,$ and $\,|Im/e|^{\frac{1}{3}}v$, at the extremum of $\varphi$ and $\tilde{\xi}$. The deepest minimum corresponds to solution (\ref{['eq:NonSusycMin']}). The cut of the plot at $V=0$ is due to the constraint $e^{\varphi(b,v)}>0$.