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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ArXiv ePrint: 2002.10147
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Gadde, A., Sharma, T. Constraining conformal theories in large dimensions. J. High Energ. Phys. 2022, 35 (2022). https://doi.org/10.1007/JHEP02(2022)035
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DOI: https://doi.org/10.1007/JHEP02(2022)035