- #1
eherrtelle59
- 25
- 0
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.
For instance, take the β function with coupling g_s
\frac{dg^2_s}{d\ln M} = -\frac{14}{16\pi^2}g^4_s
The solution is \frac{1}{g^2_s}=\frac{14}{16\pi^2} \ln(M/M')
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?
For instance, take the β function with coupling g_s
\frac{dg^2_s}{d\ln M} = -\frac{14}{16\pi^2}g^4_s
The solution is \frac{1}{g^2_s}=\frac{14}{16\pi^2} \ln(M/M')
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?