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Sphalerons and Other Saddles from Cooling

M. García Pérez
P. van Baal
Journal / Anthology

Nuclear Physics B
Year: 1994
Volume: 429
Page range: 451-473

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. Es+34.148(2) and Es+72.605(2) for the twisted and periodic case. Remarkably, the magnetic field for the periodic sphaleron satisfies at all points TrB2x=TrB2y=TrB2z.

*Science > Physics > Quantum Physics