Dyonic bound states

TL;DR

This paper explores the properties, stability, and phase transitions of fermion-monopole bound states, revealing their dependence on UV symmetries, mass terms, and the theta parameter, and connecting them to the concept of semitons.

Contribution

It provides a detailed analysis of dyonic bound states, their formation, stability conditions, and their relation to the Witten effect and asymptotic states, highlighting new insights into their quantum properties.

Findings

Bound states depend on UV symmetries, mass terms, and theta.

Phase transitions can occur, altering stability of bound states.

Bound state radii diverge in the massless limit, leading to asymptotic states.

Abstract

We study (multi) fermion - monopole bound states, many of which are the states that dyons adiabatically transition into as fermions become light. The properties of these bound states depend critically on the UV symmetries preserved by the fermion mass terms, their relative size, and the value of $\theta$. Depending on the relative size of the mass terms and the value of $\theta$, the bound states can undergo phase transitions as well as transition from being stable to unstable. In some simple situations, the bound state solution can be related to the Witten effect of another theory with fewer fermions and larger gauge coupling. These bound states are a result of mass terms and symmetry breaking boundary conditions at the monopole core and, consequently, these bound states do not necessarily have definite quantum numbers under accidental IR symmetries. Additionally, they have binding energies that are $\mathcal{O}(1)$ times the fermion mass and bound state radii of order their inverse mass. As the massless limit is approached, the bound state radii approach infinity, and they become new asymptotic states with odd quantum numbers giving a dynamical understanding to the origin of semitons.