Sphalerons in composite and non-standard Higgs models

Understand

After the discovery of the Higgs boson and the rather precise measurement of all electroweak boson's masses the local structure of the electroweak symmetry breaking potential is already quite well established.

• However, despite being a key ingredient to a fundamental understanding of the underlying mechanism of electroweak symmetry breaking, the global structure of the electroweak potential remains entirely unknown.
• The existence of sphalerons, unstable solutions of the classical action of motion that are interpolating between topologically distinct vacua, is a direct consequence of the Standard Model's $\mathrm{SU}(2)_L$ gauge group.
• Nevertheless, the sphaleron energy depends on the shape of the Higgs potential away from the minimum and can therefore be a litmus test for its global structure.