Mellin Bootstrap for Scalars in Generic Dimension

TL;DR

This paper employs the Mellin bootstrap framework to analyze scalar conformal field theories in various dimensions, revealing the absence of perturbatively interacting scalar CFTs in dimensions greater than six.

Contribution

It applies the Mellin bootstrap method to higher-dimensional scalar CFTs, providing new algebraic bootstrap equations and insights into their existence.

Findings

No perturbative scalar CFTs in d>6 to second order

Mellin bootstrap effectively constrains scalar CFTs in arbitrary dimensions

Supports the idea that interacting scalar CFTs do not exist in high dimensions

Abstract

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.