Obtaining the sphaleron field configurations with gradient flow
arXiv:2003.02070 · doi:10.1103/PhysRevD.101.096014
Abstract
We propose a formalism to obtain the electroweak sphaleron, which is one of the static classical solutions, using the gradient flow method. By adding a modification term to the gradient flow equation, we can obtain the sphaleron configuration as a stable fixed point of the flow in the large flow time. Applying the method to the -Higgs model (the Weinberg angle is ) in four dimensions, we obtain the sphaleron configuration whose energy coincides with previous studies numerically. We can also show that the Chern-Simons number of the solution has a half-integer.
17 pages, 4 figures; v2: published version