Regular and Irregular Boundary Conditions in the AdS/CFT Correspondence

TL;DR

The paper addresses incorporating scalar operators with dimensions below the unitarity bound into the AdS/CFT framework by using irregular boundary conditions. It extends Klebanov and Witten's proposal by proving all-order perturbative correctness and clarifying that internal-line propagators must use a modified Green's function $\\tilde{G}$. The analysis shows that $\\phi_-$ and $\\phi_+$ are conjugate boundary data and that the generating functional is a Legendre transform $J[\\phi_+]$, reproducing the expected two-point function for $Δ= d/2-\\alpha$ while preserving the regular-BC results for $Δ= d/2+\\alpha$. The work provides a consistent, perturbatively valid method to realize AdS/CFT with irregular boundary conditions, widening the range of operators accessible via holography and highlighting the role of the conjugate boundary data and modified propagators in higher-order diagrams.

Abstract

We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.