View Single Post
Oct10-10, 06:01 PM
Sci Advisor
P: 1,685
Quote Quote by MTd2 View Post
There are 2 factors that one needs to keep track, the cosmological and newton "constants". Those form a surface to which all those infinite coupling "constants" converge too. So, it is really not impossible to find the asymptotic safe point :).
If you want to call a mathematical property a theory is up to you.
As for the SM, isn't there a divergence due the value of Higgs?
No thats not necessarily correct. The critical surface dimensionality in general depends on how many attractive directions there are. That is something that only experiment can conclusively tell you. In the approximation where you truncate all the higher derivative terms (generated by radiative corrections) and only keep the EH part, then presumably the critical surface is obviously at most 2 dimensional (depending on if the CC and Newtons constant are attractive, which they showed to be true in the original papers). In general for arbitrary many matter couplings and for arbitrarily many derivative terms, the surface dimensionality will vary in principle or is unknown. However the good news is that you only have ot make a finite number of experiments.

"As for the SM, isn't there a divergence due the value of Higgs"