Reading off the non-geometric scalar potentials via topological data of the Calabi Yau manifolds

Abstract

In the context of studying the 4D effective potentials of type IIB non-geometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level non-geometric scalar potential arising from a flux superpotential which includes the S-dual pairs of non-geometric fluxes $(Q,P)$, the standard NS-NS and RR three-form fluxes $(F_3,H_3)$ and the geometric flux ($\omega$). This `symplectic formulation' is valid for arbitrary numbers of Kähler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as hodge numbers and the triple intersection numbers) of the compactifying (CY) threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kähler- and super-potentials.

version 3: 46 pages; slight rewording in the title, improved overall presentation with lengthy eqns. shifted to two newly added appendices B and D, one more appendix A listing the symbols and notations added; to appear in PRD

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Cited by in corpus (15)

• Systematics of type IIB moduli stabilisation with odd axions
• Dictionary for the type II nongeometric flux compactifications
• Rigid nongeometric orientifolds and the swampland
• $T$-dualizing the de-Sitter no-go scenarios
• Non-geometric fluxes & tadpole conditions for exotic branes
• Symplectic formulation of the type IIA nongeometric scalar potential
• On stable type IIA de-Sitter vacua with geometric flux
• Seeking de-Sitter Vacua in the String Landscape
• Taxonomy of scalar potential with U-dual fluxes
• On the limitations of non-geometric fluxes to realize dS vacua
• Symplectic formulation of the type IIB scalar potential with U-dual fluxes
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Duality rules for more mixed-symmetry potentials
• On Formulating the Non-Geometric Scalar Potentials
• Systematic exploration of the non-geometric flux landscape