On Black Attractors in 8D and Heterotic/Type IIA Duality

TL;DR

This paper explores black attractors in 8D supergravity and their relation to heterotic/Type IIA string duality, analyzing constraints, moduli spaces, and classifications using advanced algebraic structures.

Contribution

It provides a detailed analysis of duality constraints and moduli space structures in 8D supergravity, linking geometric configurations to algebraic classifications.

Findings

Duality between heterotic on T^2 and Type IIA on surfaces {\

} moduli space characterized by SO(1,1) x (SO(2,r+2))/(SO(2)xSO(r+2))

Classification of solutions using affine Kac-Moody algebra Dynkin diagrams

Abstract

Motivated by the study of black attractors in 8D supergravity with 16 supersymmetries, we use the field theory approach and 8D 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 {\Sigma}2. We investigate the two constraints that should be obeyed by {\Sigma}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 SO(1,1)x((SO(2,r+2))/(SO(2)xSO(r+2))) where r stands for the rank of the gauge symmetry G_{r} of the 10D heterotic string on T^2. The remarkable cases r=-2,-1,0 as well as other features are also investigated.