Type II/F-theory superpotentials with several deformations and $ \mathcal{N} = 1 $ mirror symmetry

Abstract

We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized hypergeometric GKZ system which determines the off-shell superpotential and its analytic properties under deformation. Explicit expressions for the N = 1 superpotential for families of type II/F-theory compactifications are obtained for a list of multi-parameter examples. Using the Hodge theoretic approach to open-string mirror symmetry, we obtain new predictions for integral disc invariants in the A model instanton expansion. We study the behavior of the brane vacua under extremal transitions between different Calabi-Yau spaces and observe that the web of Calabi-Yau vacua remains connected for a particular class of branes.1 See ref.[31] for recent progress from matrix factorizations. 2 See also refs. [32,33,34,35] for further examples and discussions.

On D-brane moduli stabilisation

“…For instance, one may wonder which other D-branes (or NS5-branes) may develop a superpotential of the form (1.1). In particular one may compare our results with the open-closed superpotentials involving D5-branes [43,[48][49][50][51][52][53][54]. Also, it would be interesting to see how the D7-brane Wilson line stabilisation of section 5 is generalised to (p, q)-7-branes in F-theory compactifications.…”

Off-shell D-brane/F-theory effective superpotentials and Ooguri–Vafa invariants of several compact Calabi–Yau manifolds

“…The GKZ system of X 14 (1, 3, 3, 3, 5) have been calculated in [20]. We cite the charge The off-shell superpotential being the integration of special periods of subsystem [20] …”

“…Some result are listed in the table 1. We don't list the result of d 3 = 0, being the chose instanton numbers, for its equal to the on-shell result in [20]. [12] It is unfortunate that this chosen of charge vectors is inappropriate, because once all nonzero integral number in any column of these three l have same sign the fractional result is unavoidable.…”

“…The selection of mori cone which spanned by the charge vectors is quite crucial at different limit for the integral property of Ooguri-Vafa invariant. In our example we choose the same additional charge vector in [20] which's exist due to the divisor. The result is ont integral because of unappropriate chosen of additional charge vector.…”

Holomorphic couplings in non‐perturbative string compactifications

“…Thus, we can interpret the seven-brane superpotential as a special case of the five-brane superpotential, where a description of the five-brane curve Σ in terms of seven-brane flux [F 2 ] = Σ is applicable [80], see also [100,120,121,123,[126][127][128][129] for a similar use of the seven-brane superpotential. 21 It is important to emphasize that the five-brane charge is only locally non-trivial, i.e.…”