On The Stability of Non-Supersymmetric Attractors in String Theory

TL;DR

The paper analyzes non-supersymmetric attractors in Type IIA string theory on Calabi–Yau manifolds within the two-derivative action. By employing group-theoretic methods, the stability problem is reduced to a STU-like model, enabling determination of the mass spectrum and higher-order corrections along massless directions. For D0-D4 black holes, the quadratic massless modes are protected, and quartic corrections—computed via STU benchmarks—can determine stability, with flat directions present in STU. In D0-D6 cases, a moduli space of non-supersymmetric attractors emerges, with massless directions remaining flat and all massive modes stabilized, and the D0-D4-D6 case shows similar flatness for the massless sector after symmetry arguments and duality. Altogether, the work clarifies how higher-order corrections govern stability and how dualities constrain possible cubic and quartic terms in the effective potential.

Abstract

We study non-supersymmetric attractors obtained in Type IIA compactifications on Calabi Yau manifolds. Determining if an attractor is stable or unstable requires an algebraically complicated analysis in general. We show using group theoretic techniques that this analysis can be considerably simplified and can be reduced to solving a simple example like the STU model. For attractors with D0-D4 brane charges, determining stability requires expanding the effective potential to quartic order in the massless fields. We obtain the full set of these terms. For attractors with D0-D6 brane charges, we find that there is a moduli space of solutions and the resulting attractors are stable. Our analysis is restricted to the two derivative action.