Dictionary for the type II nongeometric flux compactifications

Abstract

We study the $T$-dual completion of the four-dimensional $\mathcal{N}=1$ type II effective potentials in the presence of (non-)geometric fluxes. First, we invoke a cohomology version of the $T$-dual transformations among the various moduli, axions and the fluxes appearing in the type IIA and type IIB effective supergravities. This leads to some useful observations about a significant mixing of the standard NS-NS fluxes with the (non-)geometric fluxes on the mirror side. Further, using our $T$-duality rules, we establish an explicit mapping among the $F$-terms, $D$-terms, tadpole conditions as well as the Bianchi identities of the two theories. Secondly, we propose what we call a set of "axionic flux polynomials", which depend on all the axionic moduli and the fluxes. This subsequently helps in presenting the two scalar potentials in a concise and manifestly $T$-dual form, which can be directly utilized for various phenomenological purposes as we illustrate in a couple of examples.

50 pages, 12 tables; arXiv admin note: text overlap with arXiv:1712.07310, arXiv:1603.08545 and arXiv:1508.01197 in the review section; version 2: typos fixed and references added; version 3: 49 pages, minor changes, published version

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• Flux Compactification
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• Gauged Double Field Theory
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Cited by in corpus (17)

• A Systematic Approach to Kähler Moduli Stabilisation
• F-theory flux vacua at large complex structure
• Systematics of type IIB moduli stabilisation with odd axions
• Rigid nongeometric orientifolds and the swampland
• $T$-dualizing the de-Sitter no-go scenarios
• Moduli stabilization with non-geometric fluxes -- comments on tadpole contributions and de-Sitter vacua
• Type IIB flux compactifications with $h^{1,1}=0$
• Systematics of perturbatively flat flux vacua
• Seeking de-Sitter Vacua in the String Landscape
• Systematics of perturbatively flat flux vacua for CICYs
• On the limitations of non-geometric fluxes to realize dS vacua
• Taxonomy of scalar potential with U-dual fluxes
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• On Formulating the Non-Geometric Scalar Potentials
• Systematic exploration of the non-geometric flux landscape
• Divisor topologies of CICY 3-folds and their applications to phenomenology