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What is a 'sphaleron' in basic terms?

  1. Feb 16, 2016 #1
    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: :


    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?
  2. jcsd
  3. Feb 16, 2016 #2


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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: [itex] k \sim \int \tilde{F}^{\mu \nu a} F_{\mu \nu}^a d^4 x[/itex].. 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 reccommend 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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