Revisiting the two formulations of Bianchi identities and their implications on moduli stabilization

Abstract

In the context of non-geometric type II orientifold compactifications, there have been two formulations for representing the various NS-NS Bianchi-identities. In the first formulation, the standard three-form flux ($H_3$), the geometric flux ($\omega$) and the non-geometric fluxes ($Q$ and $R$) are expressed by using the real six-dimensional indices (e.g. $H_{ijk},{\omega }_{ij}{}^k,Q_i{}^{jk}$ and $R^{ijk}$), and this formulation has been heavily utilized for simplifying the scalar potentials in toroidal-orientifolds. On the other hand, relevant for the studies beyond toroidal backgrounds, a second formulation is utilized in which all flux components are written in terms of various involutively even/odd $(2,1)$- and $(1,1)$-cohomologies of the complex threefold. In the lights of recent model building interests and some observations made in arXiv:0705.3410 and arXiv:0709.2186, in this article, we revisit two most commonly studied toroidal examples in detail to illustrate that the present forms of these two formulations are not completely equivalent. To demonstrate the same, we translate all the identities of the first formulation into cohomology ingredients, and after a tedious reshuffling of the subsequent constraints, interestingly we find that all the identities of the second formulation are embedded into the first formulation which has some additional constraints. In addition, we look for the possible solutions of these Bianchi identities in a detailed analysis, and we find that some solutions can reduce the size of scalar potential very significantly, and in some cases are too strong to break the no-scale structure completely. Finally, we also comment on the influence of imposing some of the solutions of Bianchi identities in studying moduli stabilization.

version 3: 46 pages; improved presentation with some clarifications added on page 18; to appear in JHEP

References in corpus (33)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
• Gauged Double Field Theory
• Duality orbits of non-geometric fluxes
• deSitter vacua from uplifting D-terms in effective supergravities from realistic strings
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• Towards Universal Axion Inflation and Reheating in String Theory
• $\overline{D3}$ and dS
• De Sitter from T-branes
• Emergence of Spontaneously Broken Supersymmetry on an Anti-D3-Brane in KKLT dS Vacua
• A Flux-Scaling Scenario for High-Scale Moduli Stabilization in String Theory
• D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation
• The Challenge of Realizing F-term Axion Monodromy Inflation in String Theory
• Type-IIA flux compactifications and N=4 gauged supergravities
• Toroidal Orientifolds in IIA with General NS-NS Fluxes
• Global String Embeddings for the Nilpotent Goldstino
• Towards Axionic Starobinsky-like Inflation in String Theory
• D-Terms from Generalized NS-NS Fluxes in Type II
• On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
• Algebras and non-geometric flux vacua
• The Flux-Scaling Scenario: De Sitter Uplift and Axion Inflation
• de Sitter String Vacua from Perturbative Kahler Corrections and Consistent D-terms
• Combining Universal and Odd RR Axions for Aligned Natural Inflation
• Non-geometric flux vacua, S-duality and algebraic geometry
• Relating Double Field Theory to the Scalar Potential of N=2 Gauged Supergravity
• De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications
• Dimensional oxidation and modular completion of non-geometric type IIB action
• Implementing odd-axions in dimensional oxidation of non-geometric type IIB action
• De Sitter Uplift with Dynamical Susy Breaking
• A symplectic rearrangement of the four dimensional non-geometric scalar potential
• On modular completion of generalized flux orbits
• Single-step de Sitter vacua from non-perturbative effects with matter

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• Non-geometric backgrounds in string theory
• $P$ fluxes and exotic branes
• Systematics of type IIB moduli stabilisation with odd axions
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• 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
• 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
• Inflating in perturbative LVS: Global Embedding and Robustness
• Seeking de-Sitter Vacua in the String Landscape
• On Missing Bianchi Identities in Cohomology Formulation
• 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
• Assisted Fibre Inflation in Perturbative LVS
• Reading-off the non-geometric scalar potentials with U-dual fluxes
• Systematic exploration of the non-geometric flux landscape
• On Formulating the Non-Geometric Scalar Potentials
• Duality rules for more mixed-symmetry potentials