Connections between conformal field theory and particle physics I'm wondering if one could use conformal field theory to predict any facts in (experimental) particle physics?
I think CFT shares some similarities with QCD, but I'm not sure if one could use CFT to predict any effects in QCD.
 A: Well, you should clarify, what do you mean by predicting facts in QCD by means of CFT. CFT studies the correlation functions, relationships between them by means of conformal bootstrap. QCD is not a conformal theory even if we are dealing with negligible masses of fermions, due to the existence of scale - $\Lambda_{QCD}$.
The theories experiencing continious phase transitions are conformal for the critical temperature $T = T_c$. However, for QCD for zero chemical potential there is no phase transition with the increase of temperature, but a crossover at the temperature $T \sim 150$ MeV. With the inclusion of chemical potential at a certain magnitude, there emerges the line of phase transition. And at the value, where this line begins, there is presumably critical point, where the transition is of second order, where the CFT might find applications.
Also, maybe you have meant the $\mathcal{N}=4$ SYM theory, which is conformal (superconformal) which is definitely described in terms of CFT, and it, indeed, shares some common properties with QCD.
