Renormalization group functions of quantum field theories are key to understanding underlying critical phenomena. We can calculate these RG functions and the corresponding critical exponents for a variety of scalar and gauge theories in different dimensions. The connection of fixed points in d-dimensional theories with strict 2-dimensional CFTs gives a foundation for connecting field theories across the dimensions. This can be verified by calculating critical exponents in the large N expansion. I will specifically look at the Landau-Ginzburg-Wilson model in $6-2\epsilon$ dimensions which can be connected to the 4-dimensional theory of the same name. I will also briefly describe some computational techniques used in this calculation and present some recent results.