Real–time dynamics of a hot Yang-Mills theory: a numerical analysis

High temperature baryon number non conservation in the electroweak theory caused by the anomaly of the baryonic current is important for the understanding of the origin of baryonic matter in the universe. After the work of Ref. [1] it was realized that the baryon number nonconservation, caused by thermal field fluctuations between gauge-equivalent vacua with different winding numbers could be large in the unbroken phase of the electroweak theory. This can be tested by performing real time simulations of hot gauge theories, a task we still do not know how to perform from first principles. It is possible, however, to use classical thermal gauge theory in order to address the question [2]. The result is that transitions between vacua with different winding numbers is unsuppressed at high temperatures in the unbroken phase of the electroweak theory [3]. The effect of correctly incorporating ultraviolet thermal fluctuations has been addressed in the the theory of hard thermal loops and the effective small-momentum, low frequency theory of Bödeker (ASY-B) [4]. The soft classical fields (momentum k ≤ gT ) couple to hard currents according to