On black attractors in 8D and heterotic/type IIA duality

Motivated by the study of black attractors in 8 D supergravity with 16 supersymmetries, we use the field theory approach and 8 D supersymmetry with non trivial central charges to shed light on the exact duality between heterotic string on T 2 and type IIA on real connected and compact surfaces Σ 2 . We investigate the two constraints that should be obeyed by Σ 2 and give their solutions in terms of intersecting 2-cycles as well their classification using Dynkin diagrams of affine Kac-Moody algebras. It is shown as well that the moduli space of these dual theories is given by where r stands for the rank of the gauge symmetry G r of the 10 D heterotic string on T 2 . The remarkable cases r = −2, −1, 0 as well as other features are also investigated.