Del Pezzo Surfaces and Affine 7-brane Backgrounds

TL;DR

This paper establishes a correspondence between string junctions in affine 7-brane backgrounds and vector bundles on del Pezzo surfaces, revealing a deep link via mirror symmetry and K-theory that connects different string theory realizations.

Contribution

It constructs a novel isomorphism between string junction lattices and K-theory groups of del Pezzo surfaces, bridging Type IIB and Type IIA string theories through mirror symmetry.

Findings

Lattice of string junctions is isomorphic to K-theory of del Pezzo surfaces.

A map between states in N=2, D=4 theories with E_N symmetry is established.

SL(2,Z) symmetry acts as Fourier-Mukai transform on D-brane configurations.

Abstract

A map between string junctions in the affine 7-brane backgrounds and vector bundles on del Pezzo surfaces is constructed using mirror symmetry. It is shown that the lattice of string junctions with support on an affine 7-brane configuration is isomorphic to the K-theory group of the corresponding del Pezzo surface. This isomorphism allows us to construct a map between the states of the N=2, D=4 theories with E_N global symmetry realized in two different ways in Type IIB and Type IIA string theory. A subgroup of the SL(2,Z) symmetry of the \hat{E}_9 7-brane background appears as the Fourier-Mukai transform acting on the D-brane configurations realizing vector bundles on elliptically fibered B_9.