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On Wikipedia, there is an article on Moduli(Physics). The link is the following https://en.wikipedia.org/wiki/Moduli_(physics) . What captures me is Higgs and Coulomb Branch. If you click the links on Wikipedia, for these you notice that there is no article for them. A Google search yields research papers non-suited for the novice. What is a SIMPLE model that illustrates these concepts. Preferably written for a Physics high school student or College Freshman.Is there a video, or tutorial I can be directed to which goes over the concepts and operational steps?

  1. I am interested in an operational definition (e.g . . A "X" is a "P" with . . . .)

  2. A simple worked out example (e.g In a simple theory of "X" coupled to "Y" . . . in d dims the "K" branch is a . . . . and here are steps that get you from "M" to "Z")

  3. I like diagrams and animations because I am an idiot ( e.g The vectors from point "l" are the . . .)

I think I can benefit most from simple expository media, with the ideas explicitly stated. I have to confess, I don't want to read a full book.I am human. I can go over a page or two long article, but I love videos. I am aware of prerequisites to gain such understanding.

Qmechanic
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1 Answers1

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Oh hi there . . .

Symmetry breaking happens

  • You can break gauge symmetry via the higgs mechanism. Sometimes different types of higgs fields transform differently.

    a) Coulomb phase : broken to a product of U(1) factors

    b) Higss Phase : the breaking was so hardcore, all U(1) factors died

    Consider N =2 super Yang-Mills as @Dirac,@ACuriousMind, Wikipedia ( and perhaps me, depending on if you had coffee) have pointed out "The moduli space locally factors as the product of the moduli of a vector multiplet and a hypermultiplet, and the first factor is called the Coulomb branch and the second the Higgs branch" -- ACuriousMind

@Diracology also points out that this kind of thinking helps characterize the phases of super-symmetric gauge theory.

For the full treatment ncatlab has a link of references. Some of them might even address @AcuriousMind's comment about meaning outside of N = 2.

Notably Hiraku Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional =4\mathcal{N} = 4 gauge theories, I (arXiv:1503.03676)

References

1.) What's the Coulomb Branch and why is it important?

2.)https://en.wikipedia.org/wiki/Higgs_phase

3.) What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

4.) https://ncatlab.org/nlab/show/Coulomb+branch

5.) https://en.wikipedia.org/wiki/Spontaneous_symmetry_breaking

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