| Summary: | Abstract In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension D, the four-point function of identical scalar operators ϕ with scaling dimension ∆ ϕ such that ∆ ϕ /D < 3/4, is necessarily that of the generalized free field theory. This result follows only from crossing symmetry and unitarity. In particular, we do not impose the existence of a conserved spin two operator (stress tensor). We also present an argument to extend the applicability of this result to a larger range of conformal dimensions, namely to ∆ ϕ /D < 1. This extension requires some reasonable assumptions about the spectrum of light operators. Together, these results suggest that if there is a non-trivial conformal theory in large dimensions, not necessarily having a stress tensor, then its relevant operators must be exponentially weakly coupled with the rest.
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