Motion of Chern-Simons Number at High Temperature Under a Chemical Potential

Abstract

I investigate the evolution of finite temperature, classical Yang-Mills field equations under the influence of a chemical potential for Chern Simons number $N_{CS}$. The rate of $N_{CS}$ diffusion, ${\Gamma }_d$, and the linear response of $N_{CS}$ to a chemical potential, ${\Gamma }_{\mu }$, are both computed; the relation ${\Gamma }_d=2{\Gamma }_{\mu }$ is satisfied numerically and the results agree with the recent measurement of ${\Gamma }_d$ by Ambjorn and Krasnitz. The response of $N_{CS}$ under chemical potential remains linear at least to $\mu =6T$, which is impossible if there is a free energy barrier to the motion of $N_{CS}$. The possibility that the result depends on lattice artefacts via hard thermal loops is investigated by changing the lattice action and by examining elongated rectangular lattices; provided that the lattice is fine enough, the result is weakly if at all dependent on the specifics of the cutoff. I also compare SU(2) with SU(3) and find ${\Gamma }_{\mathrm{SU}(3)}\sim 7({\alpha }_s/{\alpha }_w{)}^4{\Gamma }_{\mathrm{SU}(2)}$.

Comments: 33 pages including figures, included with psfig. Minor rewordings, and a correction of an incorrect comment about Yang-Mills Higgs theory in Appendix A