nLab M-theory on Calabi-Yau manifolds

Idea

The KK-compactification of 11-dimensional supergravity/M-theory on Calabi-Yau manifold fibers.

On $CY_3$

For CY fibers of complex dimension 6, this yields the strong coupling version of CY-compactification of type II string theory/type II supergravity (see supersymmetry and Calabi-Yau manifolds).

Leads to D=5 supergravity effective field theory and D=5 super Yang-Mills theory.

See at 5d supergravity the section Via KK-Compactification of 11d Supergravity

See also at F/M-theory on elliptically fibered Calabi-Yau 3-folds.

On $CY_4$

• F/M-theory on elliptically fibered Calabi-Yau 4-folds

Related concepts

KK-compactification of M-theory

• M-theory on a circle

• M-theory on 8-manifolds/on Spin(7)-manifolds

• M-theory on G₂-manifolds

  • G₂-MSSM

• M-theory on Sp(1)-manifolds

• M-theory on hyperbolic manifolds

• heterotic M-theory on ADE-orbifolds

• M-theory on Calabi-Yau manifolds

  • on CY2-folds

  • on CY3-folds

  • on CY4-folds

  • on CY5-folds

References

KK-Reduction of 11D SuGra on $CY^3$s to 5D SuGra

Discussion of KK-compactification of D=11 supergravity on Calabi-Yau 3-folds to D=5 supergravity (cf. M-theory on Calabi-Yau manifolds):

• Chris Hull, Paul Townsend, p 30-31 of: Unity of Superstring Dualities, Nucl. Phys. B 438 (1995) 109-137 [doi:10.1016/0550-3213(94)00559-W, arXiv:hep-th/9410167]

• George Papadopoulos, Paul K. Townsend: Compactification of $D=11$ supergravity on spaces of exceptional holonomy, Phys. Lett. B 357 (1995) 300-306 [doi:10.1016/0370-2693(95)00929-F, arXiv:hep-th/9506150]

• A. C. Cadavid, Anna Ceresole, Riccardo D'Auria, Sergio Ferrara: 11-Dimensional Supergravity Compactified on Calabi-Yau Threefolds, Phys. Lett. B 357 (1995) 76-80 [doi:10.1016/0370-2693(95)00891-N, arXiv:hep-th/9506144]

• Sergio Ferrara, Ramzi R. Khuri, Ruben Minasian: M-theory on a Calabi-Yau manifold, Phys. Lett. B 375 (1996) 81-88 [doi:10.1016/0370-2693(96)00270-5, arXiv:hep-th/9602102]

• Sergio Ferrara, Ruben Minasian, Augusto Sagnotti: Low-Energy Analysis of M and F Theories on Calabi-Yau Threefolds, Nucl.Phys. B 474 (1996) 323-342 [doi:10.1016/0550-3213(96)00268-4, arXiv:hep-th/9604097]

• Jieming Lin, Torben Skrzypek, Kellogg S. Stelle: Compactification on Calabi-Yau threefolds: Consistent truncation to pure supergravity, J. High Energ. Phys. 2025 200 (2025) [doi:10.1007/JHEP03(2025)200, arXiv:2412.00186]

See also:

• Shun'ya Mizoguchi, Nobuyoshi Ohta: More on the Similarity between $D=5$ Simple Supergravity and M Theory, Phys. Lett. B 441 (1998) 123-132 [doi:10.1016/S0370-2693(98)01122-8, arXiv:hep-th/9807111]

For 11D Sugra with M9-branes (Hořava-Witten theory):

• Andre Lukas, Burt A. Ovrut, Kellogg S. Stelle, Daniel Waldram: Heterotic M-theory in Five Dimensions, Nucl. Phys. B 552 (1999) 246-290 [doi:10.1016/S0550-3213(99)00196-0, arXiv:hep-th/9806051]

• Adam Falkowski, Five dimensional locally supersymmetric theories with branes, Master Thesis, Warsaw (1999?) $[$pdf]

Further

Via the BFSS matrix model:

• Shamit Kachru, A. Lawrence, Eva Silverstein: On the Matrix Description of Calabi-Yau Compactifications, Phys. Rev. Lett. 80 (1998) 2996-2999 [doi:10.1103/PhysRevLett.80.2996, arXiv:hep-th/9712223]

On D=5 super Yang-Mills theory from KK-compactification of M-theory on Calabi-Yau 3-folds:

• Cyril Closset, Michele Del Zotto, Vivek Saxena: Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective, SciPost Phys. 6 052 (2019) [arXiv:1812.10451, doi:10.21468/SciPostPhys.6.5.052]

• Vivek Saxena: Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study, High Energ. Phys. 2020 198 (2020) [arXiv:1911.09574doi:10.1007/JHEP04(2020)198]