Ok, I'm having some conceptual difficulty here. When discussing beta functions and the relation how these differential equations flow, I still don't quite get the difference between relevant vs. marginally relevant and irrelevant vs. marginally irrelevant.(adsbygoogle = window.adsbygoogle || []).push({});

For instance, take the β function with coupling g_s

[itex]\frac{dg^2_s}{d\ln M} = -\frac{14}{16\pi^2}g^4_s[/itex]

The solution is [itex]\frac{1}{g^2_s}=\frac{14}{16\pi^2} \ln(M/M')[/itex]

such that the theory diverges at M'. The theory's obviously asymptotically free, as when the scale M grows, the coupling g_s decreases.

So, since the beta function is negative, I know this is either irrelevant or marginally irrelevant. What's the difference?

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# Beta functions and relevant/irrelevant operators

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