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?

  • $\begingroup$ Second-year undergrad? Or second-year grad student? $\endgroup$ – G. Smith Jan 14 '19 at 3:45
  • 1
    $\begingroup$ 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 '19 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 '19 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 '19 at 4:24
  • $\begingroup$ This paper seems very relevant to your project: arxiv.org/pdf/1309.2657.pdf. $\endgroup$ – G. Smith Jan 14 '19 at 5:59

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.

| cite | improve this answer | |
  • $\begingroup$ 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 '19 at 5:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.