Mellin Bootstrap for Scalars in Generic Dimension

We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in $d>6$ dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in $d>6$ and are consistent with the intuition that no such CFTs exist.