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Context: I am a second-year (undergraduate) physics major applying for a summer research position. The investigator is working on Quiver Gauge Theories and in response to my inquiry email he told me to

"compute the HS for the Coulomb branch of 3D $\mathcal{N}=4$ $U(1)$ gauge theory with $n$ flavors."

Assuming HS is short for Hilbert Series, I think I am approaching an understanding of what the problem is asking of me, however I cannot seem to find any concrete description of what $\mathcal{N}$ refers to. Help?

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  • $\begingroup$ Second-year undergrad? Or second-year grad student? $\endgroup$ – G. Smith Jan 14 at 3:45
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    $\begingroup$ See en.wikipedia.org/wiki/N_%3D_4_supersymmetric_Yang–Mills_theory for an explanation of N. I would run away as fast as I could from this investigator if he or she is not going to spend time with you to get you up to speed. $\endgroup$ – G. Smith Jan 14 at 3:56
  • $\begingroup$ @G.Smith I'm an undergrad. The position description stated that students of all levels of knowledge are encouraged to apply, but willingness to learn is a must; therefore I suspect that this is just some test to see if I am willing to tackle a problem with which I am unfamiliar. At least, that's what I hope. $\endgroup$ – Azimuth Zero Jan 14 at 4:07
  • $\begingroup$ If the investigator is encouraging students with all levels of knowledge to apply, then I would go for it. Good luck! $\endgroup$ – G. Smith Jan 14 at 4:24
  • $\begingroup$ This paper seems very relevant to your project: arxiv.org/pdf/1309.2657.pdf. $\endgroup$ – G. Smith Jan 14 at 5:59
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In a supersymmetric gauge theory, N is the rank of the R-symmetry group. If N is 4, it means that the theory is invariant under four different but related supersymmetry transformations.

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  • $\begingroup$ I am out of my area of expertise here. If I got this wrong, I hope an expert will correct me. $\endgroup$ – G. Smith Jan 14 at 5:40

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