Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence

TL;DR

This paper demonstrates how multi-trace boundary interactions in AdS/CFT can be incorporated through generalized boundary conditions, reproducing RG effects and revealing fixed points and dualities in the dual field theory.

Contribution

It introduces a method to include multi-trace interactions in AdS/CFT via new boundary conditions, extending the correspondence beyond single-trace cases.

Findings

Reproduces boundary RG effects using modified boundary conditions.

Constructs a line of fixed points with nonperturbative duality.

Shows a flow between different quantization methods.

Abstract

We argue that multi-trace interactions in quantum field theory on the boundary of AdS space can be incorporated in the AdS/CFT correspondence by using a more general boundary condition for the bulk fields than has been considered hitherto. We illustrate the procedure for a renormalizable four-dimensional field theory with a $(\Tr \Phi^2)^2$ interaction. In this example, we show how the AdS fields with the appropriate boundary condition reproduce the renormalization group effects found in the boundary field theory. We also construct in related examples a line of fixed points with a nonperturbative duality, and a flow between two methods of quantization.