Conformal bootstrap has become an indispensable tool to understand the non-perturbative aspects of renormalization group fixed points in any space-time dimension. The recent “solution” of the d=3 critical Ising model is just one example.
In this talk, I would like to discuss the real applications of conformal bootstrap to attack the long-standing controversies on the phase transitions and critical phenomena of the frustrated spin systems in non-collinear order and the finite temperature QCD chiral transition by determining the conformal windows of O(n)xO(m) CFTs in d=3 dimensions.
The talk is based on our recent paper arXiv:1404.0489 in collaboration with Tomoki Ohtsuki.