Computing the rate of hot baryon number violation in the early universe

The baryon asymmetry in the early universe (BAU) is one of our best hints for the existence of new physics. While the standard model of particle phyiscs predicts efficient baryon-number violation at high temperatures, it lacks the amount of CP violation needed to explain the observed asymmetry. Nevertheless, the rate of baryon number violation in the standard model is an important input for any prediction of the BAU. In this talk, I will first give a primer on the physics of baryon number violation at high temperatures and its relation to the sphaleron rate and the dynamics of soft non-Abelian gauge fields. I will then outline the general strategy for computing the rate of baryon number violation in the standard model via the sphaleron rate and the role of higher-order corrections in this computation. Finally, I will present work published in 2510.20594, where I computed the leading QCD corrections to the sphaleron rate.