What is a 'sphaleron' in basic terms?

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A sphaleron is a concept in particle physics related to baryon number asymmetry in the early universe, representing a saddle point in the energy landscape of gauge and Higgs fields. It involves different vacua characterized by distinct topological charges, which can be visualized as configurations in a potential landscape, similar to the Mexican hat potential associated with the Higgs mechanism. The discussion highlights confusion around how these vacua relate to baryon transformations and the specific gauge fields involved. Understanding topological charge requires delving into advanced concepts like instantons and anomalies in quantum chromodynamics (QCD). Overall, sphalerons play a crucial role in explaining phenomena related to baryon number changes in high-energy physics.
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I'm trying to build a vague understanding of what a sphaleron is (for context: I'm reading about baryon number asymmetry in the early universe and the word keeps cropping up). I've found a paragraph that seems to get me half way there but still leaves me feeling a bit :oldconfused: :

sphaleron.png


So first of all, what is meant by "vacua which have different topological charges"?
1) When it refers to 'different vacua', should I be picturing something like the circle around the base of the 'Mexican hat' potential often seen in discussions about the Higgs mechanism?
2) What does 'topological charge' refer to?

Anyway, it says there are vacua separated by an energy barrier "given by the spaleron energy (a saddle point of the energy of gauge and Higgs fields)".
--> This is the part that I'm most confused about. I know what a saddle point is... but I'm struggling to get from here to understanding how this means a baryon changes into something else. And which gauge fields is it referring to?
 
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1. I would picture different vacua depending on the context... all in all it means that you can have 2 or more, equivalent or not, points where the potential makes a cup... This picture however has not helped me in understanding QCD vacua.
2. topological charge, well looking at the definition I found by searching: k \sim \int \tilde{F}^{\mu \nu a} F_{\mu \nu}^a d^4 x.. well these kind of constructs again appear quiet often in instantons etc... (eg such a term looks like the variation of the action due to some chiral anomaly in QCD again). I would recommend going through the Weinberg's QFT Vol2 Ch 23.1, 23.2, 23.4
It's pretty much math-like [as any topological thing]
 

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