Scalar Multiplet Recombination at Large N and Holography

TL;DR

This paper explores how coupling a free scalar to a large N CFT operator causes multiplet recombination at a non-trivial fixed point, with a dual holographic description involving boundary conditions in AdS.

Contribution

It demonstrates the phenomenon of multiplet recombination at large N and provides a holographic dual description involving boundary conditions mixing singleton and bulk fields.

Findings

Multiplet recombination occurs at a non-trivial fixed point.

Holographic dual involves boundary conditions mixing singleton and bulk fields.

The IR theory features a merged long representation in AdS.

Abstract

We consider the coupling of a free scalar to a single-trace operator of a large N CFT in d dimensions. This is equivalent to a double-trace deformation coupling two primary operators of the CFT, in the limit when one of the two saturates the unitarity bound. At leading order, the RG-flow has a non-trivial fixed point where multiplets recombine. We show this phenomenon in field theory, and provide the holographic dual description. Free scalars correspond to singleton representations of the AdS algebra. The double-trace interaction is mapped to a boundary condition mixing the singleton with the bulk field dual to the single-trace operator. In the IR, the singleton and the bulk scalar merge, providing just one long representation of the AdS algebra.