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Flux moduli stabilisation, Supergravity algebras and no-go theorems

Beatriz de Carlos, Adolfo Guarino, Jesus M. Moreno

TL;DR

The authors classify flux-induced 12d Supergravity algebras compatible with ${ m N}=1$ orientifolds on an isotropic $ ext{T}^6/( ext{Z}_2 imes ext{Z}_2)$ background in a Type IIB frame with $ar{H}_3$ and $Q$ fluxes, then map these algebras to Type IIA descriptions to apply no-go theorems for Minkowski/de Sitter vacua. They derive a dictionary between IIB and IIA contributions to the 4d scalar potential, and demonstrate that a large class of non-semisimple algebras are ruled out as sources of dS/Mkw vacua, while semisimple algebras remain viable candidates. The work yields a complete algebra list and viability table, highlighting that non-geometric flux backgrounds are the most promising arena for finding fully stabilised vacua. A follow-up numerical study is planned to locate explicit minima within the remaining viable sectors. Overall, the paper integrates algebraic classification with no-go theorems to guide the search for phenomenologically interesting flux vacua in string compactifications.

Abstract

We perform a complete classification of the flux-induced 12d algebras compatible with the set of N=1 type II orientifold models that are T-duality invariant, and allowed by the symmetries of the T^6/(Z_2 x Z_2) isotropic orbifold. The classification is performed in a type IIB frame, where only H_3 and Q fluxes are present. We then study no-go theorems, formulated in a type IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving a dictionary between the sources of potential energy for the three moduli (S, T and U) in types IIA and IIB, we are able to combine algebra results and no-go theorems. The outcome is a systematic procedure for identifying phenomenologically viable models where Mkw/dS vacua may exist. We present a complete table of the allowed algebras and the viability of their resulting scalar potential, and we point at the models which stand any chance of producing a fully stable vacuum.

Flux moduli stabilisation, Supergravity algebras and no-go theorems

TL;DR

The authors classify flux-induced 12d Supergravity algebras compatible with orientifolds on an isotropic background in a Type IIB frame with and fluxes, then map these algebras to Type IIA descriptions to apply no-go theorems for Minkowski/de Sitter vacua. They derive a dictionary between IIB and IIA contributions to the 4d scalar potential, and demonstrate that a large class of non-semisimple algebras are ruled out as sources of dS/Mkw vacua, while semisimple algebras remain viable candidates. The work yields a complete algebra list and viability table, highlighting that non-geometric flux backgrounds are the most promising arena for finding fully stabilised vacua. A follow-up numerical study is planned to locate explicit minima within the remaining viable sectors. Overall, the paper integrates algebraic classification with no-go theorems to guide the search for phenomenologically interesting flux vacua in string compactifications.

Abstract

We perform a complete classification of the flux-induced 12d algebras compatible with the set of N=1 type II orientifold models that are T-duality invariant, and allowed by the symmetries of the T^6/(Z_2 x Z_2) isotropic orbifold. The classification is performed in a type IIB frame, where only H_3 and Q fluxes are present. We then study no-go theorems, formulated in a type IIA frame, on the existence of Minkowski/de Sitter (Mkw/dS) vacua. By deriving a dictionary between the sources of potential energy for the three moduli (S, T and U) in types IIA and IIB, we are able to combine algebra results and no-go theorems. The outcome is a systematic procedure for identifying phenomenologically viable models where Mkw/dS vacua may exist. We present a complete table of the allowed algebras and the viability of their resulting scalar potential, and we point at the models which stand any chance of producing a fully stable vacuum.

Paper Structure

This paper contains 13 sections, 72 equations, 1 figure, 9 tables.

Table of Contents

  1. Motivation and outline
  2. Fluxes and Supergravity algebras
  3. The $\,\mathcal{N}=1\,$ orientifold limits as duality frames
  4. T-dual algebras in the isotropic $\,\mathbb{Z}_{2} \times \mathbb{Z}_{2}\,$ orientifolds
  5. The set of gauge subalgebras
  6. The extension to a full Supergravity algebra
  7. The flux-induced 4d effective models
  8. The canonical T-fold description
  9. The type IIA description and no-go theorems
  10. A simple no-go theorem in the volume-dilaton plane limit
  11. From the T-fold to the type IIA description
  12. Where to look for dS/Mkw vacua?
  13. Conclusions

Figures (1)

  • Figure 1: Plot of the potential energy, $\,V\,$, as a function of the modulus Im$T$. To obtain it, we have fixed all the moduli to their VEV but the lightest one, which mostly coincides with $\,\textrm{Im}T$. The magenta/dotted line (AdS) corresponds to $\,\epsilon_{2}=45\,$, the green/dashed one (Mkw) to $\,\epsilon_{2}=44.309\,$ and the red/solid line (dS) to $\,\epsilon_{2}=44\,$. Note that a tuning of the $\,\epsilon_{2}\,$ parameter is required to obtain a Minkowski vacuum ($V_{0}=0$).