Framed BPS States, Moduli Dynamics, and Wall-Crossing

TL;DR

This paper develops a supersymmetric low-energy model for BPS dyons in N=2 theories, deriving wall-crossing formulas and analyzing bound states through quantization of moduli dynamics.

Contribution

It introduces a detailed supersymmetric moduli dynamics framework for BPS states, deriving wall-crossing formulas from first principles in strongly-coupled N=2 theories.

Findings

Derived explicit wall-crossing formulas for BPS states.

Constructed BPS bound states via quantized moduli dynamics.

Identified parameters controlling the approximation validity.

Abstract

We formulate supersymmetric low energy dynamics for BPS dyons in strongly-coupled N=2 Seiberg-Witten theories, and derive wall-crossing formulae thereof. For BPS states made up of a heavy core state and n probe (halo) dyons around it, we derive a reliable supersymmetric moduli dynamics with 3n bosonic coordinates and 4n fermionic superpartners. Attractive interactions are captured via a set of supersymmetric potential terms, whose detail depends only on the charges and the special Kaehler data of the underlying N=2 theories. The small parameters that control the approximation are not electric couplings but the mass ratio between the core and the probe, as well as the distance to the marginal stability wall where the central charges of the probe and of the core align. Quantizing the dynamics, we construct BPS bound states and derive the primitive and the semi-primitive wall-crossing formulae from the first principle. We speculate on applications to line operators and Darboux coordinates, and also about extension to supergravity setting.