CERN Accelerating science

Graphical summary of the results of section \ref{Stab}.

If the orbit $O(N)\cdot \lambda_*$ has any other intersections with $\Lambda_H$ apart from $\lambda_*$, as in this figure, the fixed point $\lambda_*$ cannot be RG-stable within $\Lambda_H$.

For fixed point perturbations by quartic scalar interactions corresponding to broken symmetry generators, linearized RG naively predicts that they are marginal. Instead such deformations correspond to total derivative operators of scaling dimension larger than $d$; see the text.

The region of $(m,n)$ space satisfying the conditions $m\ge n\ge 2$, $R_{mn}\ge0$ needed to have bifundamental fixed points with real couplings. It consists of the point $m=n=2$, and of the integer points in the gray region, described by Eq.~\eqref{eqnlessm}. Notice that the allowed region around point $m=n=2$ is really a tiny triangle invisible on this scale, but $m=n=2$ is the only integer point within it.