Mellin Bootstrap for Scalars in Generic Dimension

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.

11 pages + appendices. v2: references added, few minor revisions; published version

References in corpus (5)

• Writing CFT correlation functions as AdS scattering amplitudes
• Conformal Bootstrap in Mellin Space
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Generalized Wilson-Fisher critical points from the conformal OPE
• Towards a Bootstrap approach to higher orders of epsilon expansion

Cited by in corpus (5)

• On the Polyakov-Mellin bootstrap
• Scalar CFTs and Their Large N Limits
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• Anomalous dimensions at finite conformal spin from OPE inversion
• On Mellin Amplitudes in SCFTs with Eight Supercharges