D(-1)-Instanton Superpotential In String Theory

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 $g_s,$ in F-theory compactification with a 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 $\mathcal{O}(e^{-\pi /g_s})$. 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. This result is exact in $g_s.$

v5. 36 pages. Clarifications added. Results unchanged

References in corpus (9)

• Flux Compactification
• Small Cosmological Constants in String Theory
• New F-theory lifts
• F-theory flux vacua at large complex structure
• Normalization of Type IIB D-instanton Amplitudes
• A landscape of orientifold vacua
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Euclidean D-branes in Type IIB string theory on Calabi-Yau threefolds
• Systematics of perturbatively flat flux vacua

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• D-instanton, threshold corrections, and topological string
• Fully stabilized Minkowski vacua in the $2^6$ Landau-Ginzburg model
• Stabilizing massless fields with fluxes in Landau-Ginzburg models
• Systematics of perturbatively flat flux vacua for CICYs