Timeline for How large is large $N$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2021 at 3:00 | history | tweeted | twitter.com/StackPhysics/status/1369120864030121993 | ||
| Mar 9, 2021 at 1:56 | comment | added | Chiral Anomaly | @hulsey You might be interested in these papers: SU(N) gauge theories in four dimensions: exploring the approach to N = infinity, and also SU(N) gauge theories in 2+1 dimensions. They report some interesting numerical results about how good the large $N$ approximation is, using a little bit of extrapolation. Witten's 1979 paper Baryons in the $1/N$ expansion is also required reading (maybe you've already read it), even though it only speculates about your question. | |
| Mar 8, 2021 at 23:45 | comment | added | Claudio Saspinski | The Stirling formula is a good approximation for N=4 if the factor $\sqrt{2\pi N}$ is used. Only using $Nlog(N) - N$ the difference doesn't converge to zero. But of course the relative error does converge. | |
| Mar 8, 2021 at 22:18 | comment | added | hulsey | To be clear, I'm not asking for a "solution" of Yang-Mills theory (lol). I'm asking how predictions made in the 't Hooft limit compare to actual perturbation theory calculations, and if there is a quantitative way to compare them. We definitely do know a good deal about SU(N) YM in the 't Hooft limit... | |
| Mar 8, 2021 at 22:03 | comment | added | AccidentalFourierTransform | We don't know how to solve SU(n) QCD neither for finite n, nor in the infinite limit, so we cannot say how good large-n is for n=5. We don't know what either of those theories look like, really. But, hopefully, n=3 is already "large". | |
| Mar 8, 2021 at 20:52 | history | asked | hulsey | CC BY-SA 4.0 |