On walls of marginal stability in N=2 string theories

TL;DR

This paper investigates the structure and properties of walls of marginal stability in N=2 string theories, revealing geometric features, stability conditions, and conditions under which entropy enigma decays are absent.

Contribution

It provides a detailed analysis of walls of marginal stability in N=2 theories from orbifold compactifications, including their geometric nature and implications for BPS state decays.

Findings

Walls are lines or circles in the axion-dilaton plane.

All walls intersect at a single point in the lower half-plane.

Entropy enigma decays are absent for generic moduli values.

Abstract

We study the properties of walls of marginal stability for BPS decays in a class of N=2 theories. These theories arise in N=2 string compactifications obtained as freely acting orbifolds of N=4 theories, such theories include the STU model and the FHSV model. The cross sections of these walls for a generic decay in the axion-dilaton plane reduce to lines or circles. From the continuity properties of walls of marginal stability we show that central charges of BPS states do not vanish in the interior of the moduli space. Given a charge vector of a BPS state corresponding to a large black hole in these theories, we show that all walls of marginal stability intersect at the same point in the lower half of the axion-dilaton plane. We isolate a class of decays whose walls of marginal stability always lie in a region bounded by walls formed by decays to small black holes. This enables us to isolate a region in moduli space for which no decays occur within this class. We then study entropy enigma decays for such models and show that for generic values of the moduli, that is when moduli are of order one compared to the charges, entropy enigma decays do not occur in these models.