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Journal of High Energy Physics

, 2016:85 | Cite as

M-theory potential from the G 2 Hitchin functional in superspace

  • Katrin Becker
  • Melanie Becker
  • Sunny Guha
  • William D. LinchIIIEmail author
  • Daniel Robbins
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Chern-Simons Theories M-Theory Superspaces Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Katrin Becker
    • 1
  • Melanie Becker
    • 1
  • Sunny Guha
    • 1
  • William D. LinchIII
    • 1
    Email author
  • Daniel Robbins
    • 2
  1. 1.George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and AstronomyTexas A&M UniversityCollege StationU.S.A.
  2. 2.Department of PhysicsUniversity at AlbanyAlbanyU.S.A.

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