Moduli spaces of Calabi-Yau \(d\)-folds as gravitational-chiral instantons. (English) Zbl 1457.83045
Summary: Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension \(d \leq 4\) is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations of motion of gravity with matter). More precisely, the moduli geometry of Calabi-Yau \(d\)-folds \((d \leq 4)\) describes instantons of (E)AdS Einstein gravity coupled to a standard chiral model. From the point of view of the low-energy physics of string/M-theory compactified on the Calabi-Yau \(X\), the various fields propagating on its moduli space are the couplings appearing in the effective Lagrangian.
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83E30 | String and superstring theories in gravitational theory |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
Keywords:
differential and algebraic geometry; superstring vacua; classical theories of gravity; sigma modelsReferences:
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