The Sphaleron Rate from 4D Euclidean Lattices

Abstract

We develop a new method to determine thermal activation rates, such as for bubble nucleation, topology change, \textsl{etc.}, using 4-dimensional Euclidean methods. This allows nonperturbative study on the lattice. We then investigate the strong sphaleron rate in pure-glue QCD at temperatures between 1.3 $\text{Tc}$ and 1000 $T_{\mathrm{c}}$, making contact with previous results but extending them down close to the critical temperature. The extension to full QCD will be straightforward. Limitations of the proposal (the inability to compute a certain dynamical prefactor, puzzling large-volume behavior, and the inability to treat temperatures $T<1.3T_{\mathrm{c}}$) are also discussed.

Comments: 32 pages, 14 figures, 2 tables. Updated to JHEP version