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Title:
Ricci-Flat Metrics, Gauge Connections and Scalar Lagrangians on Calabi-Yau Threefolds
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Abstract:
A brief review of physically realistic vacua in the E_8 X E_8 heterotic string theory will be given. A formula for the Yukawa couplings in terms of solutions of the gauged “twisted” Laplacian on the Calabi-Yau threefold will be discussed. These can be computed, but require explicit expressions for the metric and gauge connection on the Calabi-Yau compactification. Using methods introduced by Donaldson, it is shown how to numerically approximate the metric and gauge connection to any desired degree of accuracy and various examples are presented. For the simple case of a scalar Lagrangian, it is shown how to numerically compute the eigenmodes and several explicit examples are worked out.
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