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M-theory conifolds.

M Cvetic1, G W Gibbons, H Lü

  • 1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.

Physical Review Letters
|March 23, 2002
PubMed
Summary
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New G2 metrics (D7) bridge M-theory and string theory via Kaluza-Klein reduction. These metrics allow deeper studies into topology change and mirror symmetry in M-theory.

Area of Science:

  • Theoretical Physics
  • String Theory and M-Theory
  • Differential Geometry

Background:

  • Seven-dimensional manifolds with G2 holonomy are crucial for connecting M-theory and string theory.
  • Kaluza-Klein reduction of these manifolds leads to six-dimensional Calabi-Yau manifolds.
  • Understanding topology change and mirror symmetry is key in M-theory.

Purpose of the Study:

  • To find first-order equations for a novel family of G2 metrics, termed D7 metrics.
  • To explore the relationship between these new D7 metrics and the resolved conifold.
  • To facilitate a more profound investigation of topology change and mirror symmetry within M-theory.

Main Methods:

  • Derivation of first-order equations for the new G2 metrics (D7).
  • Analysis of the S3 x S3 principal orbits of the D7 metrics.

Related Experiment Videos

  • Comparison of D7 metrics at weak string coupling to the resolved conifold, and B7 metrics to the deformed conifold.

    • Main Results:

    • Identification of a new family of G2 metrics (D7) with S3 x S3 principal orbits.
    • Demonstration that D7 metrics relate to the resolved conifold at weak string coupling.
    • Characterization of a nontrivial parameter in D7 metrics that governs the squashing of an S3 bolt.

    Conclusions:

    • The D7 metrics offer a new avenue for studying topology change and mirror symmetry in M-theory.
    • These metrics are generally asymptotically locally conical with a non-singular circle action.
    • The findings provide a deeper understanding of the interplay between different theoretical frameworks in physics.