Abstract
We embed the component fields of eleven-dimensional supergravity into a superspace of the form X × Y where X is the standard 4D, N = 1 superspace and Y is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of Y . It contains a natural candidate for a G 2 structure on Y , and being a complex of superforms, defines a superspace Chern-Simons invariant. Adding to this a natural generalization of the Riemannian volume on X × Y and freezing the (superspin- \( {\scriptscriptstyle \frac{3}{2}} \) and 1) supergravity fields on X, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. In this approximation the action is the sum of the superspace Chern-Simons term and a super-space generalization of the Hitchin functional for Y as a G 2-structure manifold. Integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. The latter reproduces the Einstein-Hilbert term on Y in a form due to Bryant.
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ArXiv ePrint: 1611.03098
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Becker, K., Becker, M., Guha, S. et al. M-theory potential from the G 2 Hitchin functional in superspace. J. High Energ. Phys. 2016, 85 (2016). https://doi.org/10.1007/JHEP12(2016)085
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DOI: https://doi.org/10.1007/JHEP12(2016)085