Effective superpotentials of Type II D-brane/F-theory on compact complete intersection Calabi–Yau threefolds

Abstract

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 several two-deformation moduli compact CICYs with D-branes by using the extended GKZ-system method. The discrete symmetrical groups, Z 2 , Z 3 and Z 4 , of the holomorphic curves wrapped by D-branes play the important roles in computing the superpotentials, in some sense, they are the quantum symmetries of these models.Furthermore, through the mirror symmetry, the Ooguri-Vafa invariants are extracted from the A-model instanton expansion.

Superpotentials and Geometric Invariants of Parallel/Complete Coincident/Part Coincident D-brane System on Compact Calabi-Yau Manifold

“…Further, for compact Calabi-Yau manifolds, some techniques have been evolved, e.g., mixed Hodge structure variation, Gauss-Manin connection [28,29], the blowup method [30] and the GKZ-generalized hypergeometric system for open-closed sectors. This paper we focus on is to calculate D-brane superpotentials for compact Calabi-Yau manifolds with open-closed mirror symmetry and generalized GZK system [9][10][11][12][13][14][15][16]. The dual description of the superpotential in Type-II string theory can be found in F-theory.…”

Computing parallel/coincident phase D-brane superpotentials and Type-II/F-theory duality

“…So far, most of the computations of superpotentials for the D-brane system with the compact target space are contributed by branes which are described by only one open-string deformation [4,[7][8][9][10][11][12][13]. We take the advantage of Type-II/F-theory duality, which packages all the open and closed moduli together as the complex structure moduli of the dual 4-fold M 4 to study the superpotential of the D-brane system more conveniently.…”