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Classification of Superpotentials

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Abstract

We extend our previous classification [DW4] of superpotentials of “scalar curvature type” for the cohomogeneity one Ricci-flat equations. We now consider the case not covered in [DW4], i.e., when some weight vector of the superpotential lies outside (a scaled translate of) the convex hull of the weight vectors associated with the scalar curvature function of the principal orbit. In this situation we show that either the isotropy representation has at most 3 irreducible summands or the first order subsystem associated to the superpotential is of the same form as the Calabi-Yau condition for submersion type metrics on complex line bundles over a Fano Kähler-Einstein product.

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Authors and Affiliations

  1. Jesus College, Oxford University, Oxford, OX1 3DW, United Kingdom

    A. Dancer

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    M. Wang

Authors
  1. A. Dancer
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  2. M. Wang
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Correspondence to A. Dancer.

Additional information

Communicated by G. W. Gibbons

Partly supported by NSERC grant No. OPG0009421.

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Dancer, A., Wang, M. Classification of Superpotentials. Commun. Math. Phys. 284, 583–647 (2008). https://doi.org/10.1007/s00220-008-0641-z

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  • DOI: https://doi.org/10.1007/s00220-008-0641-z

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