nLab flux compactification

Idea

Flux compactifications are Kaluza-Klein compactification where a gauge field or higher gauge field has non-trivial field strength, hence “generalized electromagnetic flux” in the fiber-spaces, whose repulsive force counteracts the collapsing force of gravity on the compact fiber spaces.

Applied to supergravity this may in particular yield perturbative string theory vacua.

One way of achieving moduli stabilization for KK-compactifications in Einstein-Maxwell theory or supergravity/string theory is to consider gauge fields and/or higher gauge fields in the compact space. Their (higher) field strength/curvature forms (“fluxes”) parameterize mass terms for the compactification moduli and hence may, under suitable conditions, stabilize them.

No-go theorems

dS No-go

Role of generalised geometry

Related concepts

• flux, flux tube, flux quantization

• moduli stabilization

• landscape of string theory vacua

• G₂-MSSM

• pure spinor

• generalised complex geometry

• generalized Calabi-Yau manifold

References

• Mariana Graña: Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91-158 [arXiv:hep-th/0509003, doi:10.1016/j.physrep.2005.10.008]

• Michael Douglas, Shamit Kachru: Flux compactification, Rev. Mod. Phys. 79 (2007) 733-796 [arXiv:hep-th/0610102, doi:10.1103/RevModPhys.79.733]

• Frederik Denef, Michael Douglas, Shamit Kachru: Physics of string flux compactifications, Ann. Rev. Nucl. Part. Sci. 57 (2007) 119-144 [hep-th/0701050, doi:10.1146/annurev.nucl.57.090506.123042]

• Frederik Denef: Introduction to flux compactifications, lecture at Summer School on Particle Physics, Cosmology and Strings, Perimeter Institute (2007) [video]

• Alessandro Tomasiello: Geometry of String Theory Compactifications: Cambridge University Press (2022) [doi:10.1017/9781108635745]

• David Prieto: Moduli Stabilization and Stability in Type II/F-theory flux compactifications [arXiv:abs/2401.13339]

Via generalized complex geometry:

• Ian Ellwood: NS-NS fluxes in Hitchin’s generalized geometry [arXiv:hep-th/0612100]

In view of F-theory:

• Frederik Denef, Les Houches Lectures on Constructing String Vacua, in String theory and the real world (arXiv:0803.1194)

• F-theory – References – Flux compactification.

See also

• Barton Zwiebach, A first course in string theory

• Raphael Bousso, Joseph Polchinski, Quantization of four-form fluxes and dynamical neutralization of the cosmological constant, JHEP 06, 006 (2000) hep-th/0004134

• T.R. Taylor, Cumrun Vafa, RR Flux on Calabi-Yau and Partial Supersymmetry Breaking, Phys.Lett. B474 (2000) 130-137 (arXiv:hep-th/9912152)

• R. Blumenhagen, B. Körs, Dieter Lüst, S. Stieberger, Four-dimensional string compactifications with D-Branes, orientifolds and fluxes, Phys. Rept. 445 (2007) 1–193, hepth/0610327.

• Mariana Graña, Flux compactifications in string theory: a comprehensive review, hep-th/0509003

• Jock McOrist, Savdeep Sethi, M-theory and Type IIA Flux Compactifications (arXiv:1208.0261)

With RR-field tadpole cancellation taken into account:

• Philip Betzler, Erik Plauschinn, Type IIB flux vacua and tadpole cancellation (arXiv:1905.08823)

See also:

• David Prieto, Moduli Stabilization and Stability in Type II/F-theory flux compactifications [arXiv:2401.13339]

• Minjae Cho, Manki Kim, A Worldsheet Description of Flux Compactifications [arXiv:2311.04959]

On non-geometric flux vacua:

• Ralph Blumenhagen, A. Deser, E. Plauschinn, F. Rennecke, Bianchi identities for non-geometric fluxes: from quasi-Poisson structures to Courant algebroids, arXiv:1205.1522

• D. Mylonas, Peter Schupp, Richard Szabo, Membrane sigma-models and quantization of non-geometric flux backgrounds, arxiv/1207.0926

See also:

• Hiroki Imai, Nobuhito Maru, Toward Realistic Models in $T^2\!/\!\mathbb{Z}^2$ Flux Compactification [arXiv:2311.10324]