# High Energy Theory Seminar

*,*Massachusetts Institute of Technology

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One of the profound challenges in string theory is to understand vacua of string theory with a small number of supercharges. As an intermediate step, one can first study four-dimensional N=1 supersymmetric compactifications of string theory to attain more computational control. In this context, we study non-perturbative superpotential generated by D(-1)-branes in type IIB compactifications on orientifolds of Calabi-Yau threefolds. To compute D-instanton superpotential, we utilize F-theory compactification on toric complete intersection elliptic Calabi-Yau fourfolds. To obtain the weakly coupled type IIB description, we take the Sen-limit, but at finite string coupling, with a restriction that all D7-brane stacks 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. With this result, we finally show that in the global Sen-limit, superpotential of the underlying type IIB compactification does not receive D(-1)-instanton contributions.

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