On the Electric Charge of Monopoles at Finite Temperature

TL;DR

This paper demonstrates that the electric charge formula for non-Abelian monopoles, originally derived at zero temperature, remains valid at finite temperature when considering CP violation and gauge degrees of freedom.

Contribution

It extends the Witten formula for dyon charge to finite temperature, accounting for gauge degrees of freedom and CP violation effects.

Findings

Witten formula holds at finite temperature

Electric charge of monopoles remains unchanged with temperature

Careful gauge treatment confirms theoretical consistency

Abstract

We calculate the electric charge at finite temperature $T$ for non-Abelian monopoles in spontaneously broken gauge theories with a CP violating $\theta$-term. A careful treatment of dyon's gauge degrees of freedom shows that Witten formula for the dyon charge at $T=0$, $ Q = e(n - \theta/2\pi) $, remains valid at $T \ne 0$.