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arXiv · hep-lat/9403026

Sphalerons and Other Saddles from Cooling

Margarita Garcia Perez·Pierre van Baal
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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. $\cE_s=34.148(2)$ 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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Margarita Garcia Perez, Pierre van Baal. 1994-03-29. Sphalerons and Other Saddles from Cooling. https://doi.org/10.1016/0550-3213(94)00332-7

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