Sphalerons and Other Saddles from Cooling

Abstract

We describe a new cooling algorithm for SU(2) lattice gauge theory. It has any critical point of the energy or action functional as a fixed point. In particular, any number of unstable modes may occur. We also provide insight in the convergence of the cooling algorithms. A number of solutions will be discussed, in particular the sphalerons for twisted and periodic boundary conditions which are important for the low-energy dynamics of gauge theories. For a unit cubic volume we find a sphaleron energy of resp. ${\text{cE}}_s=34.148(2)$ and ${\text{cE}}_s=72.605(2)$ for the twisted and periodic case. Remarkably, the magnetic field for the periodic sphaleron satisfies at all points $\text{Tr}{B}_x^2=\text{Tr}{B}_y^2=\text{Tr}{B}_z^2$.

Comments: 18 p, 6 figs appended (uuencoded) (figs 4 and 6 in Mathematica format, containing raw data. If you like movies, replace Show[...] by ShowAnimation[Table[Plx[i],{i,1,12}]]. Have fun!)