Communications in Mathematical Physics

, Volume 359, Issue 2, pp 535–601 | Cite as

Effective Action from M-Theory on Twisted Connected Sum G 2-Manifolds

  • Thaisa C. da C. Guio
  • Hans Jockers
  • Albrecht Klemm
  • Hung-Yu Yeh
Article

Abstract

We study the four-dimensional low-energy effective \({\mathcal{N}=1}\) supergravity theory of the dimensional reduction of M-theory on G 2-manifolds, which are constructed by Kovalev’s twisted connected sum gluing suitable pairs of asymptotically cylindrical Calabi–Yau threefolds X L/R augmented with a circle S 1. In the Kovalev limit the Ricci-flat G 2-metrics are approximated by the Ricci-flat metrics on X L/R and we identify the universal modulus—the Kovalevton—that parametrizes this limit. We observe that the low-energy effective theory exhibits in this limit gauge theory sectors with extended supersymmetry. We determine the universal (semi-classical) Kähler potential of the effective \({\mathcal{N}=1}\) supergravity action as a function of the Kovalevton and the volume modulus of the G 2-manifold. This Kähler potential fulfills the no-scale inequality such that no anti-de-Sitter vacua are admitted. We describe geometric degenerations in X L/R , which lead to non-Abelian gauge symmetries enhancements with various matter content. Studying the resulting gauge theory branches, we argue that they lead to transitions compatible with the gluing construction and provide many new explicit examples of G 2-manifolds.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Thaisa C. da C. Guio
    • 1
  • Hans Jockers
    • 1
  • Albrecht Klemm
    • 1
  • Hung-Yu Yeh
    • 1
    • 2
  1. 1.Bethe Center for Theoretical PhysicsPhysikalisches Institut der Universität BonnBonnGermany
  2. 2.Max Planck Institute for MathematicsBonnGermany

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