Versal deformations and superpotentials for rational curves in smooth threefolds

Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds with Three Deformations

We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory compactification on the relevant Calabi-Yau fourfolds in the weak decoupling limit. We also compute the Ooguri-Vafa invariants from A-model expansion with mirror symmetry, which are related to the open Gromov-Witten invariants.

D-branes, obstructed curves, and minimal model superpotentials

In this short note we apply methods of Aspinwall-Katz to compute superpotentials of D-branes wrapped on more general obstructed rational curves in Calabi-Yau threefolds. We find an a priori unexpected match between superpotentials from certain such curves and the superpotentials of Landau-Ginzburg models corresponding to minimal models.

Effective Superpotentials of Type II D-brane/F-theory on Compact Complete Intersection Calabi-Yau Threefolds

In this paper, we extend the GKZ-system method to the more general case: compact Complete Intersection Calabi-Yau manifolds (CICY). For several one-deformation modulus compact CICYs with D-branes, the on-shell superpotentials in this paper from the extended GKZ-system method are exactly consistent with published results obtained from other methods. We further compute the off-shell superpotentials of these models. Then we obtain both the on-shell and off-shell superpotentials for sev- eral two-deformation moduli compact CICYs with D-branes by using the extended GKZ-system method. The discrete s…

双有理映射下的双曲面族的反向变形

The versal deformation of small resolutions of conic bundles over $\mathbb{P}^1\times\mathbb{P}^1$ with two sections blown down

本文研究了双曲面族的反向变形，揭示了其在 twistor 空间中的结构和变形特性。

Matrix Model Superpotentials and Calabi-Yau Spaces: an ADE Classification

We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain Intriligator and Wecht's ADE classification of $\N=1$ superconformal theories which arise as RG fixed points of $\N = 1$ SQCD theories with adjoints. The connection between matrix models and $\N = 1$ gauge theories can be seen as evidence for the Dijkgraaf--Vafa conjecture. We find that ADE superpotentials in the Intriligator--Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau's with corresponding ADE singularities. Moreover, in the additional $\Hat{O}, \Hat{A}, \Ha…

Brane superpotential and local Calabi-Yau manifolds

We briefly report on some recent progress in the computation of B-brane superpotentials for Type II strings compactified on Calabi-Yau manifolds, obtained by using a parametrization of tubular neighborhoods of complex submanifolds, also known as local spaces. In particular, we propose a closed expression for the superpotential of a brane on a genus-g curve in a Calabi-Yau threefold in the case in which there exists a holomorphic projection from the local space around the curve to the curve itself.