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Groups and representations course of the University of Oxford

Past exam of the groups and representations course of the University of Oxford

2022

The <two-index symmetric representation> of <SU(3)> is $\mathbf6$, with <Dynkin index> $5$. Thus $n$ copies have $c(r_S)=5n$, and the supplied <beta function (physics)> is
$$
\beta(g)=-\frac{g^3}{192\pi^2}(132-5n).
$$
The strict sign condition for <asymptotic freedom> is $n<132/5=26.4$, giving
$$
\boxed{n_{\max}=26.}
$$
Indeed $132-5(26)=2>0$, while $132-5(27)=-3<0$.

Solution

Past exam of the groups and representations course of the University of Oxford / 2022 / 2 / d / ii / Solution

Past exam of the groups and representations course of the University of Oxford / 2022 / 2 / d / ii / Solution

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Past exam of the groups and representations course of the University of Oxford / 2022 / 2 / d / ii / Solution

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