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Is this paper:

Hierarchies from Fluxes in String Compactifications

equ: A.9

$ \partial_\alpha \kappa = - k_\alpha$, where $\alpha =1, ..., h_{2,1} $

What are $ k_\alpha$ ?

I’m trying to find an explicit form for Kähler potential, or from equations: 2.37 and 2.38, to find after that the Complex structure metric

$ \partial_\alpha \partial_\beta \kappa = G_{\alpha \beta}$

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