Long Range Forces and Supersymmetric Bound States

TL;DR

This paper analyzes the long-range forces between BPS particles in supersymmetric gauge theories, revealing how the spectrum of bound states changes across stability curves and identifying conditions for non-BPS states.

Contribution

It introduces a method to determine BPS and non-BPS bound states by examining the moduli space where the long-range potential is attractive, applicable at strong coupling.

Findings

Potential fixed by moduli dependence of central charges.

Spectrum restructuring occurs at marginal stability curves.

Identifies non-BPS bound states and their stability regions.

Abstract

We consider the long range forces between two BPS particles on the Coulomb branch of N=2 and N=4 supersymmetric gauge theories. The 1/r potential is unambiguously fixed, even at strong coupling, by the moduli dependence of central charges supported by the BPS states. The effective Coulombic coupling vanishes on marginal stability curves, while sign changes on crossing these curves explain the restructuring of the spectrum of composite BPS states. This restructuring proceeds via the delocalization of the composite state on approach to the curve of marginal stability. Therefore the spectrum of BPS states can be inferred by analyzing the submanifolds of the moduli space where the long range potential is attractive. This method also allows us to find certain non-BPS bound states and their stability domains. As examples, we consider the dissociation of the W boson and higher charge dyons at strong coupling in N=2 SU(2) SYM, quark-monopole bound states in N=2 SYM with one flavor, and composite dyons in N=2 SU(3) SYM.