Conformal bootstrap in Mellin space

We apply conformal bootstrap ideas in Mellin space to conformal field theories with $O(N)$ symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing symmetry in Mellin space and solve the constraint equations to compute the anomalous dimension and the OPE coefficients of all operators quadratic in the fields in the epsilon expansion. This allows us to reproduce the known results and derive new results up to $O(\epsilon^3)$. Most of the results for the cubic anisotropy case we quote appear to be unexplored. For the O(N) case we also study the large N limit in general dimensions and reproduce the known results at the leading order in 1/N.