Toroidal Orientifolds in IIA with General NS-NS Fluxes

Abstract

Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T^6/Z_4.

arXiv comment59 pages, references added

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• De Sitter hunting in a classical landscape
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• On Classical de Sitter Vacua in String Theory
• Universal de Sitter solutions at tree-level
• Non-geometric backgrounds in string theory
• Moduli Stabilization and Cosmology of Type IIB on SU(2)-Structure Orientifolds
• A note on obstinate tachyons in classical dS solutions
• Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory
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• de Sitter extrema and the swampland
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• D-Terms from Generalized NS-NS Fluxes in Type II
• dS Supergravity from 10d
• Non-geometric flux vacua, S-duality and algebraic geometry
• Rigid D6-branes on T6/[Z(2)xZ(2M)xOmegaR] with discrete torsion
• $P$ fluxes and exotic branes
• Systematics of Type IIA moduli stabilisation
• Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization
• No-scale supersymmetry breaking vacua and soft terms with torsion
• Dimensional oxidation and modular completion of non-geometric type IIB action
• Dictionary for the type II nongeometric flux compactifications
• Rigid nongeometric orientifolds and the swampland
• $T$-dualizing the de-Sitter no-go scenarios
• Reading off the non-geometric scalar potentials via topological data of the Calabi Yau manifolds
• Moduli stabilization with non-geometric fluxes -- comments on tadpole contributions and de-Sitter vacua
• A symplectic rearrangement of the four dimensional non-geometric scalar potential
• Non-geometric fluxes & tadpole conditions for exotic branes
• Type IIB flux compactifications with $h^{1,1}=0$
• On modular completion of generalized flux orbits
• Revisiting toric SU(3) structures
• Symplectic formulation of the type IIA nongeometric scalar potential
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• Seeking de-Sitter Vacua in the String Landscape
• Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation
• On Missing Bianchi Identities in Cohomology Formulation
• Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds
• Lie algebroids, non-associative structures and non-geometric fluxes
• Taxonomy of scalar potential with U-dual fluxes
• On the limitations of non-geometric fluxes to realize dS vacua
• Heterotic Flux Attractors
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• The Generalised Geometry of Type II Non-Geometric Fluxes Under T and S Dualities
• Hypermoduli Stabilization, Flux Attractors, and Generating Functions
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Systematic exploration of the non-geometric flux landscape
• Duality rules for more mixed-symmetry potentials