Obtaining the sphaleron field configurations with gradient flow

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 $SU(2)$-Higgs model (the Weinberg angle ${\theta }_W$ is $0$) 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.

arXiv comment17 pages, 4 figures; v2: published version

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Cited by in corpus (5)

• The Electroweak Sphaleron in a strong magnetic field
• Q-Balls in the presence of attractive force
• Quartic Gradient Flow
• Perturbative analysis of the Wess-Zumino flow
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking