Abstract
We study the non-perturbative superpotential generated by D(-1)-branes in type IIB compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. To compute the D-instanton superpotential, we study F-theory compactification on toric complete intersection elliptic Calabi-Yau fourfolds. We take the Sen-limit, but with finite gs, in F-theory compactifications with the restriction that all D7-branes are carrying SO(8) gauge groups, which we call the global Sen-limit. In the global Sen-limit, the axio-dilaton is not varying in the compactification manifold. We compute the Picard-Fuchs equations of elliptic Calabi-Yau fourfolds in the global Sen-limit, and show that the Picard-Fuchs equations of the elliptic fourfolds split into that of the underlying Calabi-Yau threefolds and of the elliptic fiber. We then demonstrate that this splitting property of the Picard-Fuchs equation implies that the fourform period of the elliptic Calabi-Yau fourfolds in the global Sen-limit does not contain exponentially suppressed terms mathcal{O}left({e}^{-pi /{g}_s}right) . With this result, we finally show that in the global Sen-limit, the superpotential of the underlying type IIB compactification does not receive D(-1)-instanton contributions.
Highlights
We argue that understanding the D-instanton superpotential is important
We study the non-perturbative superpotential generated by D(-1)-branes in type IIB compactifications on orientifolds of Calabi-Yau threefold hypersurfaces
To compute the D-instanton superpotential, we study F-theory compactification on toric complete intersection elliptic Calabi-Yau fourfolds
Summary
F-theory compactification on an elliptic Calabi-Yau fourfold Y4 provides a non-perturbative handle on string compactifications [31]. This non-perturbative control is achieved by the geometrization of D7-branes and the running axio-dilaton [31, 33]. Provided that F-theory compactification on Y4 admits a Sen-limit [30, 34], one can compute nonperturbative gs corrections to weakly coupled type IIB string compactifications via F-theory.. We will review the Sen-limit and superpotential in F-theory. We will study the F-theory superpotential in the Sen-limit to argue that the bare D-instanton superpotential in weakly coupled type IIB string theory is encoded in the classical flux superpotential
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