Sphalerons and other saddles from cooling

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. \cE_s=34.148(2) and \cE_s=72.605(2) for the twisted and periodic case. Remarkably, the magnetic field for the periodic sphaleron satisfies at all points \Tr B_x~2=\Tr B_y~2=\Tr B_z~2.

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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!)

gauge field theory: SU(2)
lattice field theory
field equations: sphaleron
energy: sphaleron
boundary condition
saddle-point approximation
field equations: instanton
numerical calculations: Monte Carlo

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