On the internal structure of dyons in ${\cal N}=4$ super Yang-Mills theories

TL;DR

This paper constructs approximate models of dyons in ${ m extbf{N}=4}$ super Yang-Mills theories using low energy effective actions, revealing their molecule-like internal structure with charge cores, especially near lines of marginal stability.

Contribution

It introduces an approximate field configuration approach for multi-center dyons, linking brane prong descriptions with string web pictures, and explores their internal structure near marginal stability.

Findings

Dyons exhibit molecule-like internal structures with charge cores.

Approximate configurations are more accurate near lines of marginal stability.

String webs with internal faces are also discussed.

Abstract

We use the low energy effective $U(1)^r$ action on the Coulomb branch of ${\cal N}=4$ super Yang-Mills theory to construct approximate field configurations for solitonic dyons in these theories, building on the brane prong description developed in hep-th/0101114. This dovetails closely with the corresponding description of these dyons as string webs stretched between D-branes in the transverse space. The resulting picture within these approximations shows the internal structure of these dyons (for fixed asymptotic charges) to be molecule-like, with multiple charge cores held together at equilibrium separations, which grow large near lines of marginal stability. Although these techniques do not yield a complete solution for the spatial structure (i.e. all core sizes and separations) of large charge multicenter dyons in high rank gauge theories, approximate configurations can be found in specific regions of moduli space, which become increasingly accurate near lines of marginal stability. We also discuss string webs with internal faces from this point of view.