nLab
associative submanifold

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Definition

A 3-dimensional submanifold Σ 3X 7\Sigma_3 \hookrightarrow X_7 of a G2-manifold X 7X_7 is called associative if it is a calibrated submanifold, hence if the canonical 3-form ϕ\phi of the G 2G_2-manifold (tangent space-wise the associative 3-form) restricts to the volume form on Σ 3\Sigma_3.

Accordingly a 4-dimensional submanifold Σ 4X 7\Sigma_4 \hookrightarrow X_7 is called coassociative if it is a calibrated submanifold with respect to the coassociative 4-form Xϕ\star_X \phi.

Application in string theory

In M-theory on G2-manifolds,

References

  • Ian Weiner, Associative 3-manifolds in 7\mathbb{R}^7, 2001 (pdf)

  • Selman Akbulut, Sema Salur, Associative submanifolds of a G 2G_2-manifold (pdf)

  • Damien Gayet, Smooth moduli spaces of associative submanifolds (arXiv:1011.1744)

Discussion of wrapped branes on associative 3-cycles is in

Further discussion specifically of M5-branes wrapped on associative 3-cycle which are either the 3-sphere or a hyperbolic 3-manifold is in

Last revised on April 3, 2019 at 09:21:13. See the history of this page for a list of all contributions to it.