$\mathcal{N}=4$ Super-Yang-Mills (SYM) theory is the maximally supersymmetric gauge theory in four dimensions and is an excellent playground to investigate new techniques in amplitude and Wilson loop calculations.

From what I could gather, $\mathcal{N}=4$ SYM is usually conformal, but apparently there exists a so called "Coulomb branch" of the theory on which it is not conformal and possesses very different properties. I find it very hard to find a pedagogical introduction into what exactly this "Coulomb branch" is. Perhaps someone here knows of a good learning resource to read up on this topic? Thanks for any suggestion!


Therminology follows from vacuum expectation value of scalar fields in SUSY multiplet. In Coulomb phase gauge symmetry broken by vev: $SU(N) \to U^{N-1}(1)$. In suprconformal phase gauge group is not broken.

For more details, I recomend you chapter 10.2 in Bertolini lectures Lectures on Supersymmetry.

About N=4 you can consult chapter 3.1 Supersymmetric Gauge Theories and the AdS/CFT Correspondence.


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