Duality Between String Junctions and D-Branes on Del Pezzo Surfaces
Kenji Mohri, Yukiko Ohtake, Sung-Kil Yang
TL;DR
The paper addresses how local mirror symmetry for del Pezzo surfaces within Calabi–Yau threefolds connects 5D ${\cal N}=1$ theories with exceptional symmetry to IIB affine ${\widehat{E}}_N$ 7-brane backgrounds and D-branes on del Pezzo surfaces. It computes Seiberg–Witten periods and the mirror map to relate string junction charges to RR charges, then establishes a precise correspondence between ${\widehat{E}}_N$ junction lattices and D-brane charge lattices via the central charge: $Z(p,q;n)=p a(z)-q a_D(z)+n s$, and translates these into the del Pezzo geometry through a two-step mirror map involving the holomorphic three-form periods and the Kähler parameters $t,t_d$. The main contributions are the explicit construction of the duality maps between junction charges and D-brane central charges, the matching of monodromies and instanton data with geometric invariants, and the extension to the ${\widehat{E}}_9$ case. This work provides a robust framework for translating stability and CMS analyses of brane configurations across the IIB/IAM dual pictures, facilitating deeper understanding of the E-type theories in compactified settings.
Abstract
We revisit local mirror symmetry associated with del Pezzo surfaces in Calabi-Yau threefolds in view of five-dimensional N=1 E_N theories compactified on a circle. The mirror partner of singular Calabi-Yau with a shrinking del Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a D3-brane. Evaluating the mirror map and the BPS central charge we relate junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This enables us to determine how the string junctions are mapped to D-branes on del Pezzo surfaces.