The document discusses using the renormalization group to build a "tower" of connected field theories across dimensions, starting from known 2-dimensional conformal field theories. It focuses on analyzing the O(N) x O(m) Landau-Ginzburg-Wilson model in 6 dimensions, which is connected to the 4D theory through a Wilson-Fisher fixed point. Perturbative calculations and the large N expansion are used to calculate critical exponents and check that the theories are in the same universality class. Studying higher dimensional theories could provide insight into physics beyond the Standard Model.