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One-modulus Calabi-Yau fourfold reductions with higher-derivative terms. (English) Zbl 1390.83343

Summary: In this note we consider M-theory compactified on a warped Calabi-Yau four-fold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kähler modulus and determine the resulting three-dimensional Kähler potential and complex coordinate. The logarithmic form of the corrections suggests that they might admit a physical interpretation in terms of one-loop corrections to the effective action. Including only the known terms the no-scale condition in three dimensions is broken, but we discuss caveats to this conclusion. In particular, we consider additional new eight-derivative terms in eleven dimensions and show that they are strongly constrained by compatibility with the Calabi-Yau threefold reduction. We examine their impact on the Calabi-Yau fourfold reduction and the restoration of the no-scale property.

MSC:

83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
53B35 Local differential geometry of Hermitian and Kählerian structures

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