Degeneracy of Decadent Dyons

TL;DR

This paper presents a new physical derivation of the degeneracy of quarter-BPS dyons in $ =4$ super Yang-Mills theory, confirming previous index calculations and extending insights to $ =2$ theories and string theory contexts.

Contribution

It introduces a simple physical approach to derive dyon degeneracies, aligning with known index results and clarifying relations between field theory dyons and string theory counting functions.

Findings

Degeneracy matches index computations in all known cases.

Decadent dyons are stable only in certain moduli space regions.

Method applies to $ =2$ gauge theories and string theory dyons.

Abstract

A quarter-BPS dyon in $\mathcal{N}=4$ super Yang-Mills theory is generically `decadent' in that it is stable only in some regions of the moduli space and decays on submanifolds in the moduli space. Using this fact, and from the degeneracy of the system close to the decay, a new derivation for the degeneracy of such dyons is given. The degeneracy obtained from these very simple physical considerations is in precise agreement with the results obtained from index computations in all known cases. Similar considerations apply to dyons in $\mathcal{N}=2$ gauge theories. The relation between the $\mathcal{N} =4 $ field theory dyons and those counted by the Igusa cusp form in toroidally compactified heterotic string is elucidated.